Measuring the impact of information aggregation mechanisms:An experimental investigation

Moez BennouriGroupe ESC Rouen

Henner GimpelKarlshrue University

Jacques RobertHEC Montréal and CIRANO

April 10, 2009

Abstract

This paper uses an experimental methodology to measure the effectiveness of different infor-mation aggregation mechanisms (IAMs) in providing useful information to imperfectly informedeconomic agents. Subjects bid for a risky asset in common value multi-unit uniform price auc-tions game. They have access to: (1) their private signals about the final value of the riskyasset, or (2) their private signals and the information generated by an IAM. We use two types ofIAMs: a market-based in which subjects can trade a risky asset (which value is highly correlatedwith the auctioned asset) before the auction, and a cheap talk IAM in which agents can an-nounce a signal to their competitors. We find that market-based IAMs allow better informationtransmission than cheap-talk IAMs. However, this better information is only partially exploitedby subjects in their bidding strategies. Comparison of bidding strategies shows that subjectsare more concerned with their competitive position in the auction rather than with the winner’scurse.

1 Introduction

Information aggregation mechanisms (IAMs hereafter) are intended to enhance information trans-

mission between market participants, or to provide predictions about future events. They may be

used as decision or predictive mechanisms.1 Many mechanisms were designed in practice and in

academia to achieve these goals. The Iowa Electronic Market (IEM) designed different market-

based IAMs by offering betting contracts on the issue of different US presidential elections. Chen

and Plott (2002) report on the use of a market-based IAM in a business environment to forecast

sales at Hewlett-Packard. Companies around the world now offer "prediction market" based on

financial, political or similar current events. These include the Hollywood Stock Exchange (US),

Intrade (IRL), NewsFuture (US) and Pro:Kons (AT).2

Initial public offerings of new equity (IPOs) and sales of Treasury bonds are natural examples

where different types of IAMs are used to aggregate information about valuations of new shares. The

bookbuilding process in IPOs (Sherman, 2005), the German pre-IPO market (Aussenegg et al, 2006,

and Löffler et al, 2005), the when-issued markets for treasury securities (Nyborg and Sundaresan,

1996) and the U.K. introduction procedure of new listings (Derrien and Kecskés, 2007), are examples

of IAMs designed in these markets.

It is largely acknowledged that IAMs, in particular market-based, provide agents with accurate

predictions (Wolfers and Zitzewitz, 2004). However, to the best of our knowledge, no study addresses

the impact of the existence of these mechanisms on subsequent strategic behavior of agents and the

way the information provided by IAMs interacts with agents’ private information.

This paper addresses these issues. We design a laboratory experiment in which we study the

way the information provided by IAMs is integrated in agents’ bidding behavior in a multi-unit

common-value uniform-price auction. The experiment contains three different treatments: (1) A

simple auction treatment where subjects participate in a series of multi-unit common value uniform-

price auctions; (2) A simple auction preceded by a market-based IAM in which subjects can trade

a risky asset which value is highly correlated with the auctioned asset; and (3) a simple auction

preceded by a cheap-talk IAM in which subjects can share their private information within a cheap-

talk game. The first treatment is a benchmark for the bidding behavior of agents in a private

information environment. Comparison of this treatment with those preceded by IAMs will help

separate the effects of the information transmitted by IAMs as well as the distortions that may1See Berg et al. (2001) and Hanson (1999).2In October 2007, the Prediction Market Business Association was launched (http://www.pmindustry.org).

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appear because of the existence of such mechanisms. In each treatment, subjects are asked to

submit bids (demand curves) in a multi-unit common value auction where they compete to obtain

units of the risky asset. Participants’ strategies will depend on their information about the value of

the asset and their behavior will reflect the way they appreciate the information they have acquired

prior to the auction.

In order to investigate the way the level of uncertainty affects subjects’ strategies, we run our

experiment within different levels of uncertainty. Also, for each auction, subjects participate in a

private information and a public information auction. Indeed, after submitting their bids and before

getting the outcome of the auction, subjects observe a public signal that aggregates all available

private signals and are asked to make new bids given this new information. The difference between

bids in private and symmetric public information auctions should be attributed to the only existence

of uncertainty and not to agents’ specific preferences.3

In pure common value multi-unit auctions, the strategic behavior of bidders is dictated by a

trade-off between the winner’s curse and the desire to make profits by winning a large share of

the auctioned good at the lowest price. While the existence of the winner’s curse will lead to less

aggressive bidding, bidders will be tempted to outbid their competitors in order to increase profits.

The outcome of this trade-off is utterly affected by the level of uncertainty. The level of uncertainty

in our experiment changes exogenously, by setting two different levels for private and public signals

received by subjects, and endogenously by introducing IAMs as channels that may allow a reduction

of uncertainty.

A major difficulty with common value multi-unit auctions is the large set of strategies available

to bidders. Contrary to unit demand auctions where bidders compete only through prices, bidders

in multi-unit auctions compete through quantity and prices. This dramatically increases the set

of possible strategies and leads to a multiple equilibria problem. With IAMs, the set of possible

strategies for subjects is even larger and the multiple equilibria problem is exacerbated. Because

of this, we derive the different sets of strategies that may arise and test for the occurrence of

these strategies and their effect on auction outcomes. Furthermore, we use the public information

environment as a benchmark for subjects’ strategic behavior instead of a theoretical equilibrium

outcome.

Comparison between market-based and cheap talk mechanisms shows the effectiveness of the

former to aggregate information. For auction outcomes we find that prices in cheap talk auctions are3See Lundholm (1991) for a discussion of the benefits of this dual market procedure.

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higher than the expected value conditional on all available information reflecting the fact that cheap

talk rounds worsened the perceived level of uncertainty and led to a higher level of winner’s curse

problem. This problem is more important the higher is the level of exogenous level of uncertainty

in the game. Subjects in market based auctions where the least affected by the winner’s curse

confirming their effectiveness in transmitting information.

However analysis of bidding behavior shows that subjects’ inverse demand functions are flatter

in market-based auctions reflecting a more aggressive bidding in these auctions. We cannot however

attribute this to the lower uncertainty in market-based auctions since subjects seem to be unaware

of the quality of the information transmitted. Aggregate demand functions in all auctions do not

respond to changes of private signals’ quality. This reflects the importance of the competitive

argument compared to the winner’s curse effect for subjects’ bid behavior.

These results suggest that market-based IAMs allow the transmission of information to markets

but the existence of strategic behavior when this information is used may mitigate the effect of

decreasing uncertainty on market performances. The use of such mechanisms as decision tools

should be carefully considered because of the potential behavioral distortions linked to the mere

existence of these mechanisms.

The paper is organized as follows. In the next section, we identify the different strands in

literature with which our paper is linked. Then, In section 3, we describe our experimental design.

Basically, subjects are invited to participate in multi-unit common value uniform-price auctions

under different information settings. In Section 4, we present the theoretical background for our

experimental environment and provide testable hypotheses. Section 5 contains the analysis of the

subjects’ behavior in the IAM stages. In section 6, auction outcomes (prices and allocations) as well

as bidding behavior of subjects in different treatments are analyzed and compared. Some concluding

remarks and political issues are provided in section 7. All tables and figures are in the Appendix.

2 Related literature

Theoretical models dealing with uniform-price common value multi-unit auctions predict the exis-

tence of multiple equilibria featuring high levels of underpricing and arbitrarily low revenues for the

seller (Wilson, 1979, Back and Zender, 1993, and Wang and Zender, 2002). When subjects demand

functions are continuous, this result holds independently of the level of uncertainty. Kremer and

Nyborg (2004a, 2004b), show that discrete demand functions and well-designed allocation rules

can considerably decrease the level of underpricing. In our experimental environment, subjects are

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asked to submit discrete demand functions and we use a pro-rata allocation rule. Consequently,

our study may be seen as an analysis of the equilibria that may occur when agents are required to

choose from a limited set of strategies.

Our paper is also related to the existing debate about selling mechanisms in IPOs. A common

feature of newly issued securities is that their valuation is subject to a large uncertainty leading to

the well documented underpricing. Several mechanisms used in practice aim to reduce uncertainty

and consequently to lessen the level of underpricing. The bookbuilding mechanism is basically a

way for firms (and their underwriters) to gather, from institutional investors, information about

their valuations of new shares (Benveniste and Spindt, 1989). Using different arguments, Derrien

and Womack (2003) and Ausubel and Cramton (1998) suggest that well-designed auctions allow

more effective information extraction leading to lower underpricing. When-issued markets in both

IPOs (Löffler et al., 2005) and sales of treasury bonds (Nyborg and Sundaresan, 1996) are shown

to aggregate effectively the information about the market value of the issued assets. With respect

to this literature, our methodology allows a comparison of the effectiveness of different IAMs in

different conditions. Interestingly, while the literature focuses on the sales’ outcomes (mainly prices

and, actually, allocations), we study the way the extracted information, if any, would be integrated

in subsequent strategic behavior by subjects. As example of such strategic behavior related to the

existence of when-issued markets is short squeezing (Nyborg and Strebulaev, 2004). We test in our

paper the occurrence of such behavior.

In our experiment, subjects participate in uniform-price auctions. There is a debate in the

treasury auction literature about the best selling design. In this literature, theoretical (Back and

Zender, 1993), empirical (Goldreich, 2007, and Brenner et al., 2007) and experimental (Goswami

et al., 1996 and Shade et al., 2006a and 2006b) papers present different arguments for and against

the optimality of uniform-price auctions compared to discriminatory price auctions. Sade et al.

(2006b), show that the behavior of subjects in uniform-price auctions is less sensitive to subjects’

asymmetric bidding capacities. In our experiment, each subject participates in series of 10 auctions.

This creates asymmetric bidding capacities for subjects and makes the use of uniform-price auctions

more appropriate to study the impact of uncertainty on bidding behavior.

Prediction markets interested both public and private sectors after their success in providing

precise estimation of probabilities of occurrence of future events (Wolfers and Zitzewitz, 2004, and

Plott, 2000). By analyzing markets for the U.S. 1996 presidential election, Berg and Rietz (2003)

show that these prediction markets may be good support for decision making. In our paper, we also

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analyze prediction markets as decision tools and we directly compare the performances of two of

such mechanisms (market-based and cheap-talk IAMs) in their prediction as well as their decision

support functions. The cheap-talk mechanism is a natural alternative to the market-based IAM

both in the political (standard polls) and economic applications.4 Furthermore, in uniform-price

auctions, the cheap-talk mechanism offers an interesting direct test for the possible appearance of

collusive behavior by subjects as predicted by the cheap-talk literature (Farrell and Rabin, 1996).

As shown in the prediction markets literature, we find that market-based IAMs transmit much

more information about the value of the auctioned asset than cheap-talk IAMs. Though these

results suggest the superiority of market-based IAMs, we analyze the impact of this behavior on

both auction outcomes (prices and allocations) and more importantly on the bidding behavior of

agents in which case we can analyze the way the information conveyed through the cheap-talk and

market-based IAM were integrated by agents in their bidding strategies.

3 Experimental design

We ran a series of lab experiments where subjects participate in sealed-bid multi-unit auctions for

a common value asset. Our experiment contains three treatments that differ with respect to the

quantity of information (about the final value of the asset) subjects may observe before they submit

their bids. These treatments are simple auctions (SA treatment hereafter), cheap talk treatment

(CT hereafter) and market-based IAM treatment (MB treatment hereafter).

We conducted a total of 17 sessions in the LUB-C3E lab5 at the CIRANO (Montreal, Canada).

In each session, a group of seven or eight subjects participates in a series of auctions. A total of 130

subjects participated in one of the three treatments, each of them in exactly one session. Subjects

were recruited via e-mail from the student population of the Montreal region using the database of

the laboratory.

The experiment was computerized using the software z-Tree (see Fischbacher, 1999). For all

sessions, the rules of the experiment were presented to all subjects. During the presentation, subjects

were encouraged to ask clarifying questions. Presentations lasted on average 25 minutes for SA

and CT and 30 minutes for MB. Afterwards, a computerized questionnaire assured the subjects’

understanding of the rules.6 Throughout a session, participants bid in a series of auction rounds.4In some sense the bookbuilding process in IPOs may be described by a cheap-talk IAM in which the underwriter

gathers information by asking for indications of interest from institutional investors. However, because of the existenceof long-term relationships between institutional investors and underwriters these indications of interest are not so"cheap" (Benveniste and Spindt, 1989).

5LUB-C3E is the Laboratoire Universitaire Bell en Commerce Électronique et Économie Expérimentale.6Presentations and questionnaires are available upon request. The documents are in French.

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Thereby they win (and sometime lose) Experimental Monetary Units (EMU). At the end of the

session, EMU are transformed in Canadian dollars according to a fixed exchange rate announced in

advance. The average payment is around 15$CAN per hour (10$US per hour). Sessions in the SA

treatment last about 70 minutes, in the CT treatment about 80 minutes, and in the MB treatment

about 140 minutes.

In each session subjects participate in 10 rounds. Each round consists of one private information

auction and one public information auction. Thus, we employ a dual market procedure like in

Kagel and Levin (1986), Kagel, Harstad and Levin (1987) and Lundholm (1991). At the beginning

of each round, participants receive a private signal about the common value of a risky asset A.

Then they submit their bids. Afterwards, and before announcing the outcome of the first auction,

subjects observe a public signal that aggregates the informational content of all their private signals.

Subsequently, they are asked to bid again for asset A. At the end, the results of both auctions are

revealed, i.e. each subject gets to know the price and his (her) personal allocation in each of the

two auctions. In order to limit the linkage between private and public information auctions, only

one of the two auctions is used to calculate the subjects’ payoff. Which auction to use is determined

by a virtual coin flip at the end of each round. This, together with the delayed announcement

of the result from the private information auction, guarantees that the only difference between

the two auctions is our focus variable, i.e., the information structure; there is no wealth effect, no

change in the risk structure, no hedging opportunities or the like that could explain differences in

subjects’ behavior (see Friedman and Sunder, 1994). The public information auctions serve as an

extreme case. Lundholm (1991) labels this part of a dual market as artificial economy and points

out that such a setting can serve in an experiment as benchmark with which to compare the private

information result. The public information outcome is an ‘empirical definition’ of the informational

efficient outcome, and a comparison with this artificial economy allows to determine how strongly

a private information auction deviates from informational efficiency in different treatments.

Auction rules: At the beginning of each session, each subject is endowed with 600 EMU. A

bid from a participant is a set of four prices – each subject submits prices at which (s)he is ready

to buy respectively 5, 15, 25, and 35 units of asset A. Prices have to be integers between 0 and 100.

No other restriction were imposed on bids.

In order to adjust for the number of subjects which slightly differs across sessions, the total

number of units for sale in each auction, Q, is set to ten times the number of subjects. The

electronic auctioneer calculates prices and allocations as well as individual profits. All units of the

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asset A are sold at the stop-out price representing the highest market clearing price. We use a

pro-rata on the margin allocation rule in which subjects with demand above the stop-out price are

awarded in full while marginal demand at the stop-out price are prorated. There is no reserve price.

Information structure: At the beginning of each round t, it is commonly known that the

value of the asset A, vt, is uniformly distributed on the integers interval [25, 75]. The value is not

revealed to any participant before the end of the round.

Each participant i observes a private signal sit about vt. In order to make the information

problem comprehensive for subjects, the notion of private signal is explained via the analogy with

an urn containing 100 balls, vt of them red and (100−vt) blue. The private signal sit is the number

of red balls in n draws with replacements. In the beginning of each round, each subject observes

n and sit. Note that as the number of red balls in a specific draw is private information, each

participant has partial information about vt. Increasing n is equivalent to increasing the precision

of private signals. For each round, n may be either six or twelve balls. Precision is always the

same for all participants. Allowing for different precisions of signals enables us to study the way

the strategies of subjects react to changes of uncertainty.

In the second part of each round, we announce the public signal St which is the sum of subjects’

private signals, i.e. St =∑

i sit. Clearly, public information is way more precise than private

information and is at least as precise as any information subjects may gather via the existing IAM.

Information aggregation mechanisms: In CT and MB treatments, private information

auctions are preceded by information aggregation mechanisms aimed to help subjects to gather

some additional information about the final value of the asset. In the CT treatment a pre-auction

communication step is introduced. After receiving the private signal sit and before submitting a

bid, each subject is asked to announce a cheap-talk signal cit ∈ [0, n]. There is no appeal to be

truthful and the value a subject chooses for cit has no direct effect on his (her) payoff. Each subject

observes the aggregate cheap-talk Ct =∑

i cit and then submit his (her) bid.

In the MB treatment, subjects have the possibility to participate in a double-sided market and

to observe orders and trades. Each session starts with two practice trials to familiarize subjects

with double auction trading. These practice trials are not relevant for payoffs and contain only

double auctions trading.

For trading to occur in the double auctions, the initial endowment of each subject is designed

so that each subject is granted a loan of 10 units each of two financial assets A and B. Asset A is

the same as in the other treatments; it is worth vt while asset B is worth (100 − vt). Thus, the

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value of each subject’s endowment is fix irrespective of vt. If a subject keeps an equal number of

assets A and B, (s)he remains entirely protected against risk, but (s)he can, if (s)he believes it is

advantageous, exchange assets A for assets B or vice versa.

Subjects can submit, withdraw, or accept buy or sell limit orders for one unit of asset A in a

computerized continuous-time double auction. If one desires to purchase more than one unit, (s)he

needs to issue or accept more than one order. Further, as there is no numéraire in this market, all

trades are executed in exchange for units of B. Hence, if one wishes to buy one unit of A at a price

p, one has to give in exchange 100−pp units of B. The important principle to understand is that it

will be advantageous to buy (sell) units of assets A at price p if and only if the true value vt of asset

A is greater (less) than p. In order to minimize the bankruptcy risk, subjects are not allowed to

have short positions.

A trading period lasts between 210 and 300 seconds. After the first 180 seconds, the period is

extended up to a maximum of 300 seconds if the market is still active. Trading is deemed active

when a trade occurs or when a new order enters and reduces the bid-ask-spread. If neither of the

two occurs for 30 consecutive seconds, the trading period is closed. At the end of each double

auction, each subject observes his (her) net position in asset A and B. After bidding for the asset

A in both private and public information auctions and the decision of allocation and payments, the

true value of the asset is revealed and the net gains (losses) of each subject from the auction round

(including the double auction) are computed and added or subtracted from the subjects’ account.

As in the SA and CT treatments, only the outcome of one of the two multi-unit auctions (private

and public) is used to calculate the subjects’ payoff.

Table 1 summarizes the information about sessions. Overall, we ran six SA sessions, six CT

sessions and five MB sessions. In each session of the MB treatment, at least one subject went

bankrupt. The bankruptcy rule is the same across all three treatments: If a subject has a negative

experimental account balance, (s)he is asked to leave the laboratory. In total, we recorded 920

individual bids in the SA treatment (460 private and 460 public), 920 individual bids in the CT

treatment (460 private and 460 public) and 704 individual bids in the MB treatment (352 private

and 352 public). In all three treatments, subjects were accurately informed about the rules of the

experiment.

A description of the timing of the game is presented in Figure 1. In Stage 1, bidders observe the

quantity of assets to be sold and the informational set-up in the game, the number of competitors,

the rules of the game to be played in Stage 2 (if it exists) and the rules of the uniform-price auction

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in Stage 3 of the game. There are three different games played by agents: simple auctions, market-

based IAM auctions and cheap-talk IAM auctions. In simple auctions there is no Stage 2, while

market-based and cheap-talk auctions are based on IAMs in which agents may strategically choose

their actions in Stages 2 and 3 of the game. Stage 4 is played in all auctions. Before announcing

the outcome of the private information auction, an aggregate (more precise) signal is announced to

all agents and they are invited to submit again given the new information they hold. Finally, in

Stage 5, allocations and prices are displayed for both auctions.

4 Theoretical background and testable hypotheses

Bidders in multi-unit auctions compete through quantity and prices. They choose their bidding

strategy among all weakly downward sloping bid schedules. This set of potential strategies is very

large compared to the unit auctions, and leads to the existence of multiple equilibria. Also, in multi-

unit common value auctions, the strategic behavior of bidders is dictated by a trade-off between

the winner’s curse and the desire to make profits by winning a large share of the auctioned assets

at the lowest price. While the existence of the winner’s curse will lead to less aggressive bidding,

bidders will be tempted to outbid their competitors in order to increase profits. The result of this

trade-off depends on the level of uncertainty. The introduction of IAMs (market-based or cheap-

talk mechanisms) is aimed to diminish uncertainty. However, the strategic behavior of agents in

these games may distort away from this desired objective. Furthermore, this strategic behavior may

exacerbate the multiple equilibria problem for the whole game by increasing the set of potential

strategies of bidders. Our focus in this paper is not on the determination of all potential equilibria

but rather on the characterization of classes of equilibria that may occur.

In the rest of this section we characterize classes of equilibria in our four types of auctions

(symmetric public information, simple, cheap-talk, and market-based IAM auctions) and derive

testable hypotheses about the behavior of agents and its consequences on auction outcomes.

4.1 Symmetric information auctions

In these auctions, each bidder observes his own private signal as well as the aggregate signal (the

sum of all private signals). Given the information structure in our experiment, private signals are

valueless. In this symmetric information set up, the effect of the winner’s curse on bidding behavior

is reduced. This will allow us to focus on the strategic dimension of bidding.

For pure common value auctions with symmetric information, there exists a multiplicity of

equilibria in uniform-price auctions even when weakly dominated strategies are eliminated (see

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Wilson, 1979, Back and Zender, 1993 and Wang and Zender, 2002). All these equilibria may result

in an arbitrarily low stop-out (or market clearing) price and in symmetric allocation. Low stop out

prices are caused by steep demand functions submitted strategically by bidders. Intuitively, steep

demand functions increase the marginal cost of asking for larger quantities and so decreases the

incentives of the other bidders of grabbing extra quantities. This is the well known market power

hypothesis which is rejected in many empirical works (Nyborg and Sundaresan, 1996, Goldreich,

2006 and Keloharju et al., 2005). One potential explanation for this is the fact that the market power

effect heavily rely on the continuity of bidding functions. In multi-unit auctions, bidders face a trade-

off between a price improvement and an increase in allocation. In models with continuous demand

functions, bidders are reluctant to bid aggressively because they cannot increase their allocation

substantially with only a minor change in price. However with discrete demand functions, there

is a substantial increase in a bidder’s allocation when (s)he modestly increase price. Kremer and

Nyborg (2004b) show that with restriction to discrete demand functions, both by setting a price and

a quantity multiple, several equilibria with underpricing7 may arise but underpricing is bounded

above. The level of underpricing would also depend on the used allocation rule. Kremer and Nyborg

(2004a) discuss the effect of the allocation rule on the level of underpricing. They show that under a

prorata on the margin allocation rule (as we use in our experimental setup) bidders are less incited

to bid aggressively though the equilibrium prices would be closer to the true value compared to

the case of continuous demand functions.8 As in the continuous bidding functions results, the asset

should be symmetrically distributed to different bidders.

In our experimental setting we have both discrete prices, a limited number of bids and a prorata

on the margin allocation rule. Given the results of Kremer and Nyborg (2004a, 2004b) we should

expect the following:

• Prices: underpricing is strictly positive without being extremely high.

• Allocation: because of symmetric information, assets should be equally distributed amongsubjects.

• Bidding strategies: subjects bid "aggressively" and they rely exclusively on their public infor-mation signals.

In these public information auctions, the effects of the winner’s curse is reduced but does not

disappear since there is still some uncertainty about the value of the asset. This can result in less ag-7Underpricing is defined as the difference between the stop-out price and the expected value of the auctioned

assets.8In the prorata on the margin allocation rule, inframarginal demand has full priority which may inhibit price

competition. Kremer and Nyborg (2004b) show that with a simple prorata allocation rule which gives partial priorityto inframarginal demand and with a sufficiently small tick price and a sufficiently large quantity multiple, underpricingcan be made arbitrarily small.

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gressive bidding by subjects. Henceforth, the positive underpricing may be attributable to subjects’

strategic behavior or to the effect of the winner’s curse. If the main cause of underpricing is the

winner’s curse then less precise signals would result in less aggressive bids and higher underpricing.

4.2 Simple auctions

Since these auctions are those where information asymmetry between bidders is the most severe,

this case is where bidders are the most to worry about the winner’s curse. As for the symmetric

information case, different studies show that uniform-price multi-unit auctions feature the existence

of a continuum of equilibria with underpricing.9 Back and Zender (1993, Theorem 1) define a class

of symmetric equilibria for which: (1) demand functions do not vary with their private signals; (2)

the equilibrium price is arbitrarily lower than the lowest possible value of the asset; and (3) the

total quantity is equally divided among bidders. If the equilibrium described in Back and Zender

(1993) prevails, IAM mechanisms would be obsolete. But, as in the symmetric information case,

the discreetness of bidding functions as well as the allocation rule may have a dramatic effect on

equilibrium prices and allocations.

Beyond the characteristics of the equilibria in these auctions, it is important to understand the

impact of the level of information asymmetry and uncertainty on the bidding behavior of subjects

and on auction outcomes. Comparison of simple and symmetric information auctions will be helpful

to achieve this task. Theoretically, as suggested by Milgrom and Weber (1982), as uncertainty

decreases, bidders recognize that they have less to worry about the winner’s curse. They bid more

aggressively and the selling price typically increases. This linkage principle, considered as one of the

fundamental results of auction theory, was afterwards challenged by Perry and Reny (1999). They

provide a two-unit Vickrey auction example where the principle simply fails. Our experimental

analysis allows to test whether the linkage principle holds for common value uniform-price multi-

unit auctions. Analysis of the bidding behavior of subjects would allow to measure the relative

aggressiveness of subjects in simple auctions (with exogenously variable precision of private signals)

and in symmetric public information auctions.

4.3 cheap-talk auctions

In these auctions, before they bid for the risky asset, subjects observe their aggregate announced

signal, i.e. the sum of all the signals they "send" in the cheap-talk game. In standard cheap-talk

literature 10, the information content of the cheap-talk game equilibrium is necessarily related to the9See Back and Zender (1993) and, Wang and Zender (2002).

10See Rabin (1994) and more recently Gerardi (2004).

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conflict of interest between agents. Two extreme equilibria emerge. The first is a fully informative

coordination equilibrium in which subjects report honestly their private signals. Hence, the auction

bidding behavior would be the same as in symmetric information auctions. This equilibrium occurs

when agents’ preferences are sufficiently close so that truthfulness is beneficial to all agents. When

preferences are "opposite", a "bubbling" equilibrium emerges. In this equilibrium, communication

by agents is totally uninformative and the auction bidding behavior would be the same as in simple

auctions. Other partially informative equilibria may arise depending on the structure of the game

and the equilibrium concept used.

Our set up differs from the standard cheap-talk literature in several ways. First, in our envi-

ronment all agents are senders and receivers of signals (through communications) at the same time,

while in the standard literature there is in general a (more informed) sender and a (less informed)

receiver. This worsens the multiple equilibria problem. Second, like in Forsythe et al. (1999)

and the communication games literature (see Myerson, 1986 and Forges, 1990), agents report their

private signals rather than their strategies. This allows us to avoid the problems related to the

language of communication (Crawford, 1998). Because of these differences, it is important to study

the equilibrium in our set up.

Before announcing their signals, subjects will face the trade-off between truthfulness and cheat-

ing. Truthfulness will reduce uncertainty and so reduce the severity of the winner’s curse in the

subsequent auction. On the other hand, cheating (or more precisely understating) may be beneficial

in particular for agents with relatively high signals. In this case, cheating may deter the other agents

from bidding aggressively, which lowers competition and increases the expected profits of cheaters.

The winner’s curse argument leads to coordination equilibrium, while the second argument will

favor the existence of less information revealing equilibria.

It is important to check in our experimental environment whether the existing equilibrium is

fully or partially informative. A candidate class of partially informative equilibria would be based

on subjects’ strategic announcements conditional on their private signals relative values. Subjects

with high values will understate their signals (without necessarily announcing the lowest signal).

Those having relatively low signals will either report honestly their signals or overstate them in order

to mislead their competitors. Misleading may occur because subjects are concerned about relative

standing or within a dynamic strategy. Subjects with intermediate signals may behave either as

those having high signals or as those having low signals. In a symmetric equilibrium, the aggregate

signal will be high, intermediate or low. If the aggregate signal is high, then subjects observing

13

high private signal will deduce that their competitors have low (or intermediate) signals which will

induce them to be relatively less aggressive. Subjects with low and intermediate private signals will

also deduce that the true value is low which will make them less aggressive. On the other hand, low

and intermediate aggregate signals are relatively uninformative and all subjects should rely less on

these cheap-talk signals. This equilibrium is partially revealing because only high aggregate signals

convey information.

We also test the effect of uncertainty on the strategic behavior of agents in the subsequent

auctions. When uncertainty is high, subjects would be more concerned with the winner’s curse.

This would increase their motivation to exchange information.

4.4 Market-based IAM auctions

In market-based IAMs, agents participate in a double auction market where they can trade the

risky asset. There are two main features distinguishing these mechanisms from the cheap-talk

IAMs. First, contrary to cheap-talk IAMs where the set of strategies for subjects is limited to

their announcements of signals, the set of strategies in double auctions is much richer. Indeed, by

making trades, each agent should decide whether to sell or to buy, the timing of entry in the market

and whether to submit a limit order or accept an order from the order book. Second, the trading

behavior of agents will affect their final profit, contrary to the first case where talk is costless. The

bidding behavior of agents should be affected by both the informational content of the trading game

and the auction outcome.

Since we are interested in the effects of the trading behavior on the information aggregation

process, we classify equilibria according to their effectiveness with respect to this aspect. We

can detect two different classes of equilibria: manipulation equilibria and information gathering

equilibria.11

Manipulation equilibria: In these equilibria, agents’ trading behavior is aimed at misleading

their competitors. In market microstructure literature, different models show that informed traders

may strategically manipulate the information content of their early orders so as to make gains in

subsequent trading periods (Allen and Gale, 1992). Hanson et al. (2006) use an experimental

framework in which they show that manipulation fails to reduce the accuracy of prices as estimates

of the asset value. Our environment departs from this literature in two respects. First, subjects

in our experiment are not asymmetrically informed and there is no explicit incentive for market11There is a third class containing the no trade equilibrium in which agents do not trade in the first round and the

second stage equilibrium is the same as in simple auctions. We exclude this class because subjects traded in all ofthe 50 auctions we run, as we point out in the next section.

14

manipulation contrary to Hanson et al. (2006). This reduces the propensity of agents to manipulate

the market. On the other hand, the existence of subsequent auctions can create incentives for

subjects to manipulate markets in order to increase their expected profits.

Manipulation strategies purpose is to convey bad information to competitors inducing them to

bid less aggressively.12 This may be achieved by submitting sell orders at low prices (within the

existing spread) or by hitting existing limit buy orders at low prices. Though these strategies are

costly, manipulators’ hope is to recuperate their losses in the subsequent auction.

In manipulation equilibria, prices in the trading game will be relatively low and uninformative.

Informational content of the market-based IAM auction would be equivalent to simple auctions.

However, bidders in this case will be asymmetrically endowed with the risky asset because of the

executed trades. This asymmetry increases the difficulty of coordination between them in the

auction (see Sade et al, 2006b).13

Information gathering equilibria: In these equilibria, agents will base their trading in the first

stage on their private signals. Those with high signals will tend to be buyers and those with

low signals will tend to be sellers. During the trading sessions, traders will adjust their priors

about the final value of the asset given the trading history. Valuable information may be inferred

from the activity in this double-auction market and may be used in the auction game. Such

information may be transaction prices, volumes, bid-ask spreads or market depth. Informationally,

the equilibrium strategies in this game should stand between the symmetric information case and

the simple asymmetric information auctions case. The higher is the informativeness of prices in

the market-based IAM; the closer is the auction outcome to the symmetric information auction

outcome.

The informational efficiency of these equilibria will depend on the existence and intensity of some

arbitrage strategies that may be adopted. Whenever it is possible, some traders may sell the asset

at higher prices and hedge their short position in the second stage auction by submitting orders

so as to cover their positions (at prices lower than their selling prices in the IAM stage). These

strategies have no informational value and their occurrence decreases the equilibrium informational12We can think also about manipulation in the other sense (by misleadingly conveying good information). However,

because manipulation may be costly and since upward misleading competitors will negatively decrease the probabilityof winning in the auction, these strategies are less likely.

13Another type of manipulation equilibria related to the short squeezing behavior might arise. Short squeezingoccurs when some subjects take short positions on the asset A that must be covered in the auction. This situationmay oblige them to bid more aggressively and also incite other subjects to try to squeeze short sellers by biddingeven more aggressively. As a consequence, prices in the auctions might be artificially high (Nyborg and Strebulaev,2004). We exclude these equilibria from our analysis because: (1) uniform price auctions are more robust to shortsqueezing as pointed out in Chatterjea and Jarrow (1998) and; (2) short squeezing existence is related generally tothe existence of a secondary market for the auctioned securities which is not considered in our experimental set up.

15

efficiency.14

Besides the study of the occurrence of these classes of equilibria, some interesting questions

arise: What is the intensity of arbitrage trading (if it exists) and what is its impact on the price

convergence? What is the impact of this information gathering process on the auction outcome

(prices, allocations) and on subjects’ bidding behavior? And, how is the equilibrium affected by the

level of uncertainty in the market?

5 IAM behavior

In this section, we analyze the behavior of subjects in the information aggregation mechanisms in

order to focus on equilibria that are consistent with the observed behavior. For consistency, we also

compare our results to the existing literature.

5.1 Cheap-talk communication stage

Figure 2 depicts the relation between the expected value of the asset conditional on the true aggre-

gate signal and the aggregate signal announced by subjects. Clearly, the announced signal contains

roughly no information about the true aggregate signal.15 A Mincer-Zarnowitz test confirms this

result. This excludes the prevalence of a coordination equilibrium in the cheap-talk game. However,

we shall not conclude that announcements by subjects were simply bubbling without looking inside

the box by closely analyzing the behavior of subjects.

Overall, 46 subjects participated in cheap-talk sessions and submitted 460 cheap-talk announce-

ments. Truthful announcing is the most frequent behavior. However, a coordination behavior is

not likely because of the large frequency of dishonest announcement. This result is in line with

Forsythe, Lundholm and Rietz (1999) where most but not all sellers in an adverse selection setting

make dishonest announcements.16 Participants are truthful 38.3% of the time. Table 2 reports the

cheap-talk behavior of subjects in six and twelve balls rounds. Honest reporting does not depend

on the precision of private signals. However, subjects tend to understate their signals in the 12

balls rounds and to overstate their signals in the 6 balls rounds. For both cases, the difference14These strategies were detected in the German pre-IPO market where Aussenegg et al. (2006) report that institu-

tional investors typically take short positions in these markets and count on receiving shares in the primary marketsin order to cover their short positions. Nyborg and Sundaresan (1996) report that 40% of the transactions made bydealers in the U.S. when-issued markets for treasury auctions are short selling that must be covered.

15The correlation of ρ = 0.004 is not significantly different from zero.16Truthful revelation of private signal might have three main causes. First, subjects might have an intrinsic

motivation to tell the truth rather than to be dishonest. Second, truthfulness might be seen as the action requiringleast mental effort and might therefore be a (bounded) rational choice (see Payne et al. 1993). Third, truthfulrevelation corresponds to a coordination equilibrium.

16

is significant17. This behavior is consistent with the class of partial revealing equilibria discussed

in Section 3. Recall that in these equilibria high aggregate signals are more informative than low

aggregate signals. So, subjects have more incentives to announce signals that convey more infor-

mation by overstating their signals. The consequence of such behavior would be a less aggressive

bidding in the multi-unit auction and consequently lower prices in six balls rounds. It is important

to test this conjecture when we analyze the bidding behavior of subjects in order to confirm (or not)

the occurrence of the partial revealing equilibria. Whether subjects tried to benefit from the infor-

mation revealed through the cheap-talk communication round or they simply used the aggregate

announced signal without considering the strategic behavior of subjects is an interesting question.

Before making this analysis, we summarize our results for the cheap-talk rounds.18

Result 1: In cheap-talk rounds, there are neither coordination nor bubbling patterns in the

communication behavior of subjects. The most likely class of equilibria is the one with partial reve-

lation of private information. When we change the level of private signals’ precision, the behavior

of subjects is consistent with these equilibria.

5.2 Double auction

In our experiment, shares where actively traded with a minimum number of orders across the 50

trading periods equal to 19.19 Each single subject actively participated in the double auction.

The trade volume relative to the volume of the multi-unit auction varies largely across groups

and periods, it ranges from 3.3% to 63.8%. In 35 out of the overall 50 double auctions, subjects

extended the auction’s deadline by continuing to trade or lowering the bid-ask-spread at the end of

the minimum duration of 180 seconds. In 6 balls auctions, subjects made 16.4 trades on average,

which is significantly20 lower than the 24.4 average numbers of trades in 12 balls auctions. This

suggests that information gathering was not the unique motivation for trading.

Figure 3 shows that the expected value of the asset conditional on the aggregate signal (observed

by subjects) and the last trading price in each round are significantly positively correlated (ρ =

0.526).21 This observation is confirmed by a Mincer-Zarnowitz analysis. We consider the following17Binomial test on the null hypothesis of equally likely direction of dishonesty yields p-values equal to 0.007 for 6

balls treatments and 0.002 for 12 balls treatments.18We also test for the occurrence of bubbling equilibria by making finer analysis of subjects’ announcing strategies

in the cheap-talk game. This analysis lead us to exclude the occurrence of these equilibria. This analysis is availableupon request.

19In the U.S. when-issued markets of treasury auctions, Nyborg and Sundaresan (1996) show that traders who planto bid in the treasury auction are reluctant to reveal positive information in when-issued trading. Market activityin our experiment seem to contradict this observation. This may be due to the importance of uncertainty in ourenvironment contrary to the treasury auction environment.

20The p-value of the undirected Wilcoxon rank test is 0.033.21Because of the aggregate uncertainty, we use the expected value of the risky asset given the pubic signal as a

17

(OLS) regression:

E(vt|St) = α+ βPt + ε (1)

where Pt is the last transaction price at round t. The price of the last trade is used because subjects

involved in this trade have the benefit of observing all prior trades and all the information possibly

revealed.22 The sample consists of the 50 double auctions conducted in all MB sessions. The

outcome of this regression is as follows

E(vt|St) = α+ βPt

4.927(10.662)

0.906(0.212)

standard errors are in parentheses. The constant is not significantly different from zero (p-value =

0.646) and the price coefficient is not significantly different from 1 (p-value = 0.658).23 In line with

the results of previous experimental studies of double auctions with common value assets (Plott

and Sunder (1988) and Lundholm (1991) among others), this suggests that prices converge to the

expected value conditional on the aggregate information.

In order to study the convergence process, we measure for each of the 50 double auctions and for

each trade the distance – defined as the square of the difference – between the transaction price and

the expected value given the aggregate signal. We then calculate the average distance for the first

half and second half of each trading round. In 35 out of 50 rounds, the distance in the second half

is less than in the first half. So, within a trading period prices tend towards the asset’s expected

value given public information. The occurrence of this convergence is significantly non-random24

and does not depend on the precision of signals.25

All these results suggest that double auction prices provide some information and allow subjects

to share their information about the final value of the asset. This result complies with field data

reported by Löffler et al. (2005) for the German stock market. They find that final when-issued

prices are unbiased predictors of the secondary market’s opening prices. The information aggrega-

tion role of when-issued trading is corroborated by a study on U.S. treasury securities where the

when-issued market plays a price discovery role by aggregating dispersed information (Nyborg and

Sundaresan, 1996).

Finally, we analyze the possibility of manipulation behavior by agents. Hanson et al. (2006)

study manipulation in double auctions: They find that traders who are interested in high market

benchmark instead of the true value.22Averaging over the last few trades yields qualitatively the same results.23A Wald test on the joint hypothesis α = 0, β = 1, gives a p-value of 0.896. The adjusted R2 of the regression is

26.1% and the p-value of the entire regression is lower than 0.001.24Binomial test on the null hypothesis of an equal chance for convergence and divergence; p-value = 0.007.25Convergence occurred in 17 out of 25 rounds and 18 out of 25 rounds for six and twelve balls rounds respectively.

18

prices due to an auction-exogenous incentive submit higher bids than other traders. Nevertheless,

they conclude that the presence of such manipulators does not harm information aggregation and

has no significant effect on the accuracy of prices. In order to study the occurrence of manipulations

in our experiment we analyze the correlation between signals of agents and their net positions at

the end of the trading period. We find that a subject’s estimate of the risky asset’s value based on

her private signal is significantly positively correlated with her net position.26 Thus, subjects with

positive information tend to be buyers and subjects with negative information tend to be sellers.

Also, transaction prices and submitted orders are positively correlated with private signals. These

results point out the unlikeliness of manipulation behavior by subjects.

Result 2: In double auctions, the information aggregation equilibria are the most likely to

prevail. In these equilibria, prices are good estimators of the asset’s value conditional on the avail-

able information and convergence is enhanced with experience. Finally, for subjects information

aggregation is not the unique motivation for trading.

6 Auction outcomes and bidding behavior

Though market-based IAMs allow a better information transmission between subjects, we should

examine whether subjects were aware of this advantage and whether their bidding behavior reflects

this difference of information availability. Comparison between public and private information

auctions in each treatment and between private information treatments allow to assess the impact

of uncertainty on auction outcomes and on the bidding behavior of subjects.

6.1 Equilibrium outcomes

The level of uncertainty in our theoretical set-up is associated with both the precision of private

information and the effectiveness of the IAM. In theory, the higher is uncertainty the higher is the

importance of the winner’s curse which would affect both the level prices and the distribution of

allocations.

6.1.1 Prices

Since our objective is to analyze the information aggregation effectiveness of different IAMs, we

focus on relative prices defined as auction prices normalized with respect to the expected value of

the risky asset given the aggregate signal.27 Table 3 displays some statistics about the relative26Correlation of ρ = 0.333. Pearson’s product-moment correlation test on null hypothesis of zero correlation;

p-value < 0.001.27Qualitatively comparable results are obtained by normalizing equilibrium prices with the asset’s true value.

19

prices in all treatments and information conditions.

In public information auctions, prices reflect the strategic behavior of subjects as suggested in

theory. In all treatments, there is a positive average underpricing and consequently a positive profit

for subjects. As expected, there is no significant difference between the distributions of relative

prices across treatments.28 The precision of signals does not affect the level of underpricing in

public information auctions. Indeed, for each treatment there is no significant difference between

relative prices in 6 and 12 balls auctions.29 This suggests that the winner’s curse does not have

much importance in these auctions.

In private information auctions, we compare relative prices among different treatments. Table

4 displays the p-values for the Wilcoxon rank sum tests of equalities of median and for the Fligner-

Killeen test of equality of variances. Relative price are highest in the cheap-talk treatment, though

the difference is significant with relative prices in MB auctions only when private signals are less

precise. On the other hand, there is no significant difference between SA and MB auctions. Also,

in SA and MB auctions there is no significant difference between relative prices in 6 and 12 balls.

However, in CT auctions, relative prices are significantly higher in 6 than in 12 balls auctions.30 We

find similar results when we compare relative prices in private and public information auctions in

each treatment. While there are no significant differences in SA and MB auctions, relative prices in

CT auctions are significantly higher in private than in public information auctions.31 These results

are robust to the learning effect when we make the same analysis for the last five auctions in each

session.

This analysis suggests that the cheap-talk communication game seems to be associated with

the least strategic behavior of subjects. More interestingly, contrary to what is suggested by the

linkage principal, decreasing the level of uncertainty does not necessarily lead to higher prices in our

multi-unit auctions. Contrary to the result of Kagel and Levin (1986), public information in our

experiment does not incite agents to bid more aggressively nor to get higher prices on average. This

happens for all cases independently of the magnitude of uncertainty which may be seen as a proxy

for the importance of the winner’s curse to agents. In order to check the robustness of this result,

we follow Kagel and Levin (1986) which argue that the winner’s curse occurs when the aggressive28We run pairwise Wilcoxon rank sum tests to compare median relative prices across treatments and Fligner-Killeen

test to compare variances. All these tests give no significant differences.29A similar comparison based on the proportion of auctions where subjects fell prey to the winner’s curse (auctions

where relative prices are larger than 1) come off to the same conclusion.30P-values of the Wilcoxon rank sum test for SA, MB and CT auctions are 0.545, 0.286 and 0.011, respectively.31Wilcoxon signed rank tests for the null hypothesis of equilibrium prices being the same under private and public

information results in p-values > 0.5, = 0.149 and = 0.005 for SA, MB and CT auctions, respectively.

20

bidding by agents results in prices higher than the expected price conditional on all the information

available in the market. So, we measure the winner’s curse by the proportion of auctions in which

the relative price is higher than 1 (Prop. rel. price > 1 in Table 3). We apply two-sided Fisher tests

(with Yates’ continuity correction) to make pairwise comparisons of the number of auctions where

relative prices are higher than 1 in public information auctions, private information auctions and 6

and 12 balls auctions in each treatment. The results are the same as for relative prices. There is

no significant difference between public information auctions, and for private information auctions,

subjects bid more aggressively in CT auctions than in SA auctions and there is no significant

difference between MB and SA auctions. Furthermore, bids in CT auctions are more aggressive

when precision of private signals is the lowest.

Result 3: Relative prices (defined as the relative value of selling prices with respect to the ex-

pected value of shares conditional on the available information in the market) are not significantly

different across treatments in public information auctions. In private information auctions, relative

prices are significantly different only for CT auctions, where relative prices increase with uncer-

tainty. Finally, for each treatment, comparison between private and public auctions does not lead

to significant difference in MB and SA auctions. However, in CT auctions relative prices are larger

in private than in public auctions. All these results are confirmed by the analysis of the number of

auctions in which subjects fall prey to the winner’s curse, i.e., where relative prices are higher than

1.

This analysis shows that enhancing the information of subjects by introducing a market-based

IAMs or lowering the level of uncertainty does not necessarily increase the seller’s revenues. So like

in Perry and Reny (1999), the linkage principle does not hold in our multi-unit auctions. This may

be because the winner’s curse is less important in these auctions.

In IPOs, Löffler et al. (2005) analyze the impact of pre-IPO markets in Germany and find that

these markets lead to an effective, and efficient information aggregation process. They also conclude

that asymmetric information cannot explain the high level of underpricing observed in IPOs. Our

results support these observations since we also find that market-based IAMs allow for information

aggregation but that this information seems to be unimportant to explain the level of underpricing.

From the seller’s point of view, it would be naïve to conclude that cheap-talk based IAMs

will be preferred since prices in these auctions are the highest. In practice, though an IPO is a

one shot game, it establishes a long lasting relationship between the issuer and investors at the

secondary market and in subsequent offerings. Thus, an issuer that increases revenue by fostering

21

the dissemination of seemingly accurate information might do poorly in the long run once investors

realize the overpayment (Aggrawal, Krigman and Womack, 2002). Choosing a cheap-talk based

IAM will not be the best strategy for the seller if we consider some institutional aspects of IPOs or

treasury bonds.

6.1.2 Allocations

Results about relative prices suggest that subjects may have bid strategically as predicted by sym-

metric equilibria. In these equilibria subjects bid without considering their information in their

strategies and allocation is perfectly symmetric. On the other hand, the winner’s curse occurrence

may have a different impact on allocation symmetry. With higher uncertainty, bidders would be

more sensible to the winner’s curse resulting in a less aggressive bidding and consequently to more

symmetric allocations.

It is also worth noting that allocation symmetry in uniform-price multi-unit auctions is very

sensitive to subjects’ individual behavior. As a matter of fact, it takes just one aggressive bid or

one highly conservative bid to create a positive bias in the allocation asymmetry measure. This

would misleadingly result in highly asymmetric allocation creating artificially a bias that would

mitigate the impact of the level of uncertainty on the allocation symmetry.

As in Sade et al. (2006a and 2006b) and Keloharju et al. (2005) we use the Herfindahl-

Hirschman index (HH index hereafter) in order to measure the symmetry of allocations. This index

is defined as the sum of squares of allocations as percentages of the entire quantity. Also, because

of the restrictions related to the number of subjects and to the maximal number to bid for in our

experiment, we use a normalized HH index defined as follows

H =(∑n

i=1( xi10∗n)2)−Hmin,n

Hmax,n −Hmin,n(2)

where, n is the number of bidders (thus 10 ∗ n is the number of units allocated), and xi is the

allocation of bidder i. Hmin,n and Hmax,n are the un-normalized minimum and maximum values of

the HH index given the number n of bidders in the auction and the range of possible allocations.

Note that allocations are integers belonging to [0, 35] for i and that the normalized HH index

belongs to [0, 1] for all auctions independently of n. A high value (close to 1) of the normalized HH

index signals an asymmetric allocation, whereas a low value (close to 0) signals a very symmetric

allocation.

Table 5 displays the mean and standard deviation of the (normalized) HH indices for all treat-

22

ments and for 6 and 12 balls treatments separately.

As expected, normalized indices are very high in all treatments suggesting that allocations are

highly concentrated in all treatments. Comparisons between median values and variances of the HH

indices in private information treatments for all conditions produce globally insignificant differences

between treatments.32 This suggests a high concentration of allocations independently of the quality

of the available information in these auctions. For public information treatments, allocations in SA

and MB treatments are equally concentrated and are significantly more concentrated than in CT

auctions.33 Furthermore, as can be easily seen in Table 5 symmetry of allocations is higher in public

than in private CT auctions and the difference is higher when the quality of information is lower

(in the 6 balls treatments). So like in the price analysis, subjects seem to be highly affected by

uncertainty in the CT auctions compared to MB and SA auctions. This suggests a lower confidence

of subjects in the available information in CT auctions.

Result 4: Allocations are highly asymmetric in all treatments and are roughly the same in all

SA and MB auctions. However, in CT auctions, subjects seem to get more symmetric allocations in

public compared to private information auctions reflecting a higher aversion to the winner’s curse

effect.

The high asymmetry of allocations in all treatments suggest the occurrence of "asymmetric"

equilibria caused by highly aggressive bidding by some subjects. In our experiment, at least one

subject received the maximal quantity (i.e. 35 units) in more than 68% of auctions.34 The existence

of these highly aggressive trading results in asymmetric allocations in all treatments and make

the comparison with respect to the availability of information more ambiguous. Finally, allocation

concentration does not depend on the level of uncertainty in the market consistently with Keloharju

et al. (2005).

Notwithstanding the importance of using equilibrium outcomes (prices and allocations) in order

to measure the effectiveness of IAMs, looking inside the box by analyzing the strategic behavior

of subjects when they bid would provide us with more valuable information. Also, analysis of the

bidding behavior should allow to explain some of the results about prices and allocations by focusing

on the way subjects used the information provided by the IAM. Finally, this enables exploring the

existence of some strategies (such as arbitrage) that would explain some of the equilibrium outcomes.32We use the Wilcoxon rank sum test to compare median values of the normalized HH index and the Fligner-Killeen

test to compare variances. These results are robust to the experience effect and to the quality of private signals.33The p-values for the Wilcoxon rank sum test when we compare CT auctions with MB or SA auctions are <0.001

in both cases.34The proportion of auctions for which at least one subject received the maximal quantity range from 68% in public

information CT auctions to 82% for private information MB auctions.

23

6.2 Bidding behavior

Throughout our experiment, we have collected 10,176 individual bids. We use this data to examine

how bidding behavior varies across the various treatments and information conditions. Each indi-

vidual bid contains four maximal prices that the bidder is ready to pay in order to receive up to 5,

15, 25, or 35 units of the risky asset. We use these observations to estimate the aggregate demand

function in each treatment.

We begin by introducing some variables that we index by i for subjects and t for rounds. Let

x ∈ {5, 15, 25, 35} be the quantity to be purchased and E(vt|sit) be the estimate of the risky asset’s

value (vt) that a subject i may infer given her private signal at auction t (sit). Furthermore, let

E(vt|SIAMt ) be the estimate of the risky asset’s value conditional on the information provided by

the IAM when it exists. In CT auctions, this information is the aggregate cheap-talk signal; in MB

auctions, it is last trading period price. E(vt|St) is the estimated value given the public signal in

public information auctions (St). We also define ln(Wit) as the logarithm of subject i’s experimental

account balance before the beginning of auction t. In MB auctions, subjects trade shares before they

begin bidding. The net position of each subject may affect her bidding strategy. Let define Ait the

subject i’s net position of A contracts before auction t. Finally, let nt be the number of participants

in auction t.

In order to explore the different dimensions of our study, we estimate different models aimed

to measure the way subjects react to more information and to an information with better qual-

ity. Equation 6.2 presents a generic model used to estimate subjects’ bids pit using the available

information and controlling for the variable that may affect the bidding behavior of subjects.

pit = α1 + α2x+ α3E(vt|sit) + α4E(vt|St) + α5E(vt|SIAMt ) + α6ln(Wit) + α7Ait + α8nt + εit

In this estimation of the inverse demand function, α4 reflects the role of the public signal. This

variable is introduced only for public information auctions. α5 is an estimation of the impact of the

information gathered through the IAM, i.e., cheap talk and MB auctions. α7 introduces a control

variable to account for asymmetry in the initial endowment of shares after the pre-auction exchange

in the MB treatments. This model is estimated separately in the public and private information

auctions. The results of these estimations for all treatments are presented in Table 6.

In order to measure the way the bidding behavior of subjects is affected by the different dimen-

sions of enhancing the quality and quantity of information, we estimate a series of other models.

Generically, we introduce for each case a dummy variable that will be defined depending on the

24

dimension we are interested in. For private versus public information auction in each treatment,

we compare the way subjects deviate in the private information auctions from the benchmark case

represented by public information auctions. This is designed to assess the way subjects perceive the

level of uncertainty in private information auctions compared to public information auctions. The

results are displayed in columns ∆ in Table 6. Results related to the analysis of the impact of the

quality of information (six versus twelve balls) for each treatment are displayed in Table 7. Finally,

results of the comparisons between treatments are displayed in Table 8.35 For each estimation, we

focus on two coefficients: (i) the weight of each signal (private, public and IAM signal) on bidders’

behavior and (ii) the steepness of the inverse demand functions (measured by the absolute value of

the coefficient for x). Steepness of the inverse demand function measures the confidence of subjects

in their valuations. The steeper is the inverse demand function, the less confident are subjects

in their information and the less aggressive are their bids. So an increase in the quality of the

information (by announcing a public signals, designing an IAM or enhancing the quality of signals)

should decrease the steepness of the inverse demand function. The steepness of the inverse demand

function may also be affected by the strategic behavior of subjects aimed to deter competitors from

bidding more aggressively as suggested in Back and Zender (1993). In this case, steepness will not

depend on the level of uncertainty. We also analyze the way subjects use both private, the public

and inferred signals in their bids. This would measure both the consistency of their behavior and

also their perception of the quality of the information they observe.

The bidding data we analyze is panel data: different subjects constitute the cross-section dimen-

sion i and trading periods along with subject groups the time dimension t. In our experiment, we

do not observe all personal characteristics of subjects. Their risk aversion and errors in estimating

expected values are, for example, unobserved although they might influence the bidding behavior.

To account for this unobserved persistent heterogeneity of subjects and the corresponding autocor-

relation in the error term of a simple OLS regression, the models are analyzed with a random effects

feasible generalized least squares estimator.36

35All the results are robust to the learning effect. We estimate the different models using only the bidding strategiesof subjects in the last five auctions of each session. Results are roughly the same and can be provided upon request.

36As alternatives to a random effects analysis, a fixed effect estimator or a pooled regression OLS estimator couldbe used. The appropriateness of the model for our data is tested. Using the Lagrangian Multiplier test (LM test)to test the null hypothesis that there are no individual effects (see Breusch and Pagan, 1980) is rejected (p-value< 0.001 for both private and public information). This establishes that the OLS estimation is not appropriate.We also compare the fixed and random effects estimators using Hausman specification test (Hausman, 1978) to seewhether the individual effects are correlated with the regressors. The null hypothesis is that both fixed and randomeffects estimators are consistent and that only the random effects estimator is efficient. This hypothesis cannot berejected (p-value = 0.484 for private information and 0.278 for public information). So, random effects estimatorappears the most appropriate.

25

Inverse demand functions in SA auctions have some interesting patterns. Though subjects still

rely on private signals in public information auctions, the weight of private signals significantly

declines when moving from private to public information auctions (see Exp Priv coefficient in

columns 1, 2 and 3 in Table 6). However, there is no significant difference between the slopes of

inverse demand functions in the private and public information SA auctions. On the other hand, an

increase in the quality of information by moving from six to twelve balls auctions does not seem to

encourage subjects to rely more heavily on their private or public signals but, consistent with the

results of Nyborg et al. (2002), it makes bidding more aggressive since the slope of inverse demand

function becomes significantly flatter (see γ4 in Table 7).

Result 5: In SA auctions, increasing the quality of private signals affects the slope of the

inverse demand function. However, announcing a more precise public signal does affect significantly

the slope of inverse demand function. This suggests that subjects are more concerned about their

competitive behavior in the auction than about the winner’s curse

Comparisons of public information auctions between treatments confirm the fact that subjects

are more concerned about their competitive position than about the winner’s curse. If we assume

that agents pay more attention to asymmetric information problems, bidding behavior of subjects

should be similar in all public information treatments. From columns 4, 5 and 6 in Table 8, this does

not occur since bidding aggressiveness are significantly different among treatments. These differences

should be related to strategic behavior of subjects independently of information asymmetries.

Based on the poor quality of the information transmitted in the cheap talk round, inverse

demand function should be steeper in CT private information auctions than in both MB private

information auctions and CT public information auctions. Results displayed in columns 2 and 3,

Table 8 and column 6, Table 6 confirm this observation. Note also that subjects do rely positively on

the cheap talk signal (Exp IAM coefficient in column 4 Table 6) and that the quality of signals (six

versus twelve balls) does not affect the bidding behavior of subjects (see Table 7). Despite the fact

that honest reporting was not the typical strategy, subjects do rely on the aggregate announced

signal. But it seems that cheap-talk information affect negatively the way subjects perceive the

quality of their information. This is in line with Forsythe, Lundholm and Rietz (1999) in a study

of cheap-talk in an adverse selection setting. They find that a subject’s willingness to trust in

cheap-talk is unrelated to their own fraudulent behavior when talking cheaply to others. So, in CT

simple auctions, subjects rely on the cheap-talk signal though they were globally dishonest in their

reporting. This increased their perception of the level of uncertainty and resulted in steeper inverse

26

demand functions reflecting a higher concern about the winner’s curse problem. The steepness of

the inverse demand function can explain the higher level of allocation concentration and also the

higher equilibrium prices in CT auctions.37

Result 6: The inverse demand function steepness in CT auctions is consistent with the cheap-

talk game reporting behavior and the quality of the information transmitted. But, subjects seem to

inconsistently rely on the aggregate reported signal.

Compared to SA and CT private information auctions, subjects in MB private information

auctions give less importance to their private signals. With respect to SA auctions, subjects rely

on the market-based IAM (see the coefficient for ∆ Exp Priv in column 1, Table 8). However

there is no significant difference with the use of the cheap-talk round signal (∆ Exp IAM in column

3, Table 8). The importance of information does not depend on its quality (column 5, Table 7).

For bidding aggressiveness, subjects submit less steep inverse demand functions in MB auctions

(columns 1 and 3, Table 8) and the slope of the inverse demand function does not depend on the

quality of information (column 5, Table 7). These results suggest that subjects profit from the

better information transmitted by the market based IAM and consistently use it in their bidding

behavior. Comparison between private and public information MB auctions shows that subjects

rely more heavily on the most precise available signal though they still use the IAM signal even in

public information signals (columns 7, 8 and 9 in Table 6). This suggests that the market-based

IAMs play their role of information aggregation and that subjects value at least in the same way,

public signals and the signal gathered from the market based IAM. This is reflected in the use of

information and in the slopes of inverse demand functions in private and public information MB

auctions which are equally steep (see column 9, Table 6).

These observations suggest that among the candidate equilibria, the information aggregation

equilibrium is the most likely. In order to check for the existence of some arbitrage bidding, we

use the coefficient related to the net position in the asset A that may be seen as an indicator for

the existence of arbitrage trading. Arbitrageurs would be more aggressive the lower is their net

position before they bid. This behavior should be observed in both private and public information37To confirm these results, we analyze the way the cheap-talk game interacts with the bidding behavior of subjects.

We estimate the inverse demand function in the cheap-talk auctions by controlling for the reporting strategies ofsubjects. We find that subjects who understate their signals bid more aggressively than those announcing truthfullytheir signals and put a higher weight on all signals (private, public and the aggregate announced signal in thecheap-talk process). On the other hand, those overstating their signals do not seem to adopt different biddingbehavior from those announcing truthfully their signals. So, consistent with the partial information aggregationmechanism, subjects’ behavior depends on their reporting strategies. However, independently from the reportingbehavior, subjects positively rely on the aggregate announced signal despite the fact that a majority of them weredishonest. The details of this analysis are available upon request.

27

MB auctions. The coefficient for Net pos A in all tables is however significantly positive suggesting

the fact that net buyers would remain buyers by bidding aggressively and vice versa. Furthermore,

the bidding behavior in MB public information auctions does not depend on subjects’ net positions.

These observations do not support the existence of arbitrage trading. Therefore, we can state the

following:

Result 7: In MB auctions, the information gathering equilibrium prevails. In MB private

information auctions, subjects’ bids are more aggressive than in the SA and CT private information

auctions and reflect the fact that subjects are aware of the information transmitted in the double

auction game. Comparison with public information MB auctions reflects their confidence in the

quality of the transmitted signal.

7 Concluding remarks

In this paper, we analyze the impact of the existence of IAMs on the bidding behavior of agents

and on equilibrium outcomes in multi-unit common-value uniform-price auctions. We design a

laboratory experiment in which auction outcomes and the strategic behavior of different subjects

in various settings are compared. We distinguish three different treatments; (1) A simple auction

treatment where subjects participate in a series of multi-unit common value uniform-price auction;

(2) A simple auction preceded by a market-based IAM in which subjects can trade an asset which

value is highly correlated with the asset to be auctioned; and (3) a simple auction preceded by a

cheap-talk IAM in which subjects can share their private information within a cheap-talk game.

Comparison of these treatments allows to separate the effects of the existence of public information

as well as the distortions that may appear because of the existence of IAMs. Each treatment is

run within different levels of uncertainty. Also like in Lundholm (1991), we use a dual market

procedure aimed to separate asymmetric information effects on auction outcomes and subjects’

bidding behavior. This allows to understand the issue of the trade-off that subjects face in pure

common value multi-unit auctions between falling prey to the winner’s curse (because of uncertainty)

and their competitive position in the auction.

Our analysis of IAM rounds show that market-based IAMs aggregate information effectively

while cheap talk rounds conveys almost no information. Analysis of auction outcomes (prices and

allocations) does not lead to significant differences between market-based and simple auctions.

However, in cheap talk auctions, subjects fall prey to the winner’s curse more frequently. This

suggests that the cheap talk round may exacerbate uncertainty in the market and more importantly,

28

that the analysis of auction outcomes is not sufficient to understand the impact of IAM existence

on auctions. The competitive position of subjects may have been at the origin of these results.

The analysis of the bidding behavior of subjects confirm this intuition. Competition and strategic

considerations affected significantly the bidding strategies of subjects, and in some cases were much

more important than the winner’s curse effect related to uncertainty.

Multiple equilibria with arbitrarily large underpricing is an established result in the theory of

common value multi-unit auctions. The existence of IAMs exacerbates this problem because of

the large set of strategies available to participants. Our analysis shows that information aggrega-

tion equilibria in both IAMs prevail, i.e., equilibria where subjects integrated the information (if

any) transmitted by IAMs in their bidding strategies, without trying to manipulate information,

squeezing their competitors, making arbitrage or bubbling (in cheap-talk games).

Compared to simple and cheap talk auctions, bidding behavior in market based auctions are

more aggressive reflecting the effectiveness of this mechanism in transmitting information. Though,

we find that this information transmitted in market-based IAMs is partially exploited because of

subjects’ concern with their competitive position, it remains more valuable for subjects than a

simple enhancement of the exogenous level of uncertainty. This result is related to the literature

on the efficiency of public information provision in financial markets. It provides an example where

indirect information (related to trading motivations of agents) is more valuable for agents than

direct information about assets (see Bennouri et al., 2009).

Our results are also related to the IPO literature. Our experimental design may be seen as a

comparison of different IPO procedures where their performances are measured by their relative

ability to lessen information asymmetry. In a simple way, the bookbuilding procedure is similar

(in terms of information gathering process) to our cheap talk treatment since underwriters collect

information from investors by asking them to submit non binding indications of interest.38 Our

experimental results allow us to conclude the dominance of market-based IAMs in their role of

providing valuable information. This suggests that such mechanisms may be useful to lessen infor-

mation asymmetry and so to reduce underpricing. The question that remains is: How should we

implement this mechanism?

Such information aggregation mechanisms exist in several primary markets. In US treasury mar-

kets, when-issued markets operate before the issuance of treasury securities. When-issued market38Cornelli and Goldreich (2001) report that institutional investors adjust the non binding indications of interest

they announce to underwriters. This suggests that investors may try to affect the price determination process throughtheir non binding announcements.

29

is a forward market where future contracts on the securities to be issued are traded. Nyborg and

Sundaresan (1996) study empirically the role of these markets in the process of selling treasuries.

Another when-issued market, where future contracts are traded, exists for IPOs of shares in some

European countries. In general, these markets operate concurrently with a bookbuilding process.

Our results suggest that these when-issued markets play efficiently their role of information aggre-

gation and may help reduce uncertainty. These results are consistent with the empirical findings

of Löffler et al. (2005) finding that when-issued markets in Germany produce valuable information

about the stock’s secondary market value. Aussenegg et al. (2006) examine the pricing process in

the German IPO market featuring the coexistence of bookbuilding and when-issued trading. They

find that while new-issued trading allows the revelation of relevant information, it cannot supplant

bookbuilding as a source of information. Moreover, they report that underwriters begin the issuance

process by gathering information through the bookbuilding (so by collecting information from in-

vestors). This information is then publicly displayed through price ranges. Afterward when-issued

trading commences once these ranges are posted. This trading will help issuers to situate the IPO

price within ranges. Henceforth, it seems that the information-gathering role of when-issued trading

can be effective only if it is used concurrently with another direct mechanism aimed at lowering the

level of uncertainty. Without these direct mechanisms and as argued in Aussenegg et al. (2006)

when-issued markets suffer from viability problem. Indeed, when-issued markets may fail to open

(or even have repetitive breakdowns). Another weakness of these markets in the inability to avoid

transactions aimed at manipulating pricing in the IPO. In fact, heavy short selling of forward con-

tracts may cause a downward revision of IPO prices even though information about the stock’s

value is not so bad. This argument is the reason behind restrictions on when-issued trading in the

US primary stock markets.39 In our experiment, we did not detected such behavior by subjects.

39Paragraph II.F of the Securities Exchange Act Release No. 38067 (December 20, 1996) on Regulation clearlystated that: “Such short sales could result in lower offering price and reduce an issuer’s proceeds.” (see the SEC’sweb site at http//www.sec.gov/rules/final/34-38067.txt)

30

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33

Appendix

Table 1: Information structure and number of agents for different sessions

Treatment Session Number of agents† Number of balls‡

Simple Auctions (SA) SA1 8 0,1,0,0,0,0,0,1,1,1SA2 8 1,1,1,1,0,01,1,1,0SA3 8 0,1,0,0,1,01,1,0,1SA4 8 1,0,1,0,0,0,1,0,1,1SA5 8 1,0,0,0,1,1,1,0,1,1SA6 8 1,1,1,0,1,1,0,0,1,0

Cheap Talk (CT) CT1 8 0,1,0,0,1,0,0,1,1,1CT2 8 1,1,0,1,0,0,1,0,1,0CT3 8 0,1,0,0,0,1,0,1,0,1CT4 8 1,1,0,1,0,1,1,1,1,0CT5 7 0,1,0,1,0,0,0,1,0,1CT6 7 1,0,1,0,1,0,1,0,1,0

Market-based (MB) MB1 8(7) 1,0,1,1,0,0,0,0,0,1MB2 8 1,1,1,1,0,1,1,1,0,1MB3 8(7) 0,0,1,0,0,0,1,1,0,0MB4 7(5) 1,1,1,0,1,1,0,0,0,1MB5 7(6) 1,0,1,0,0,1,0,1,0,0

Note: † Because of bankruptcy, the number of agents changed during some sessions. In this case the final numberof subjects is between parentheses. ‡ 0 for 6 balls and 1 for 12 balls (10 auctions for each session). The total numberof auctioned shares is ten times the number of subjects participating in the auction.

Table 2: Frequency of individual behavioral patterns in cheap talk announcements depending on theprecision of information

Reporting All cases 6 balls 12 balls

Overstate 134 (29.1%) 78 (37.7%) 56 (22.1%)Truthful 176 (38.3%) 82 (39.6%) 94 (37.2%)

Understate 150 (32.6%) 47 (22.7%) 103 (40.7%)

total 460 (100%) 207 (100%) 253 (100%)

34

Table 3: Equilibrium prices relative to expected value of the risky asset for different treatments

SA treatment CT treatment MB treatment

Private Public Private Public Private Public

Mean rel. price 0.946 0.937 1.039 0.970 0.991 0.958Std. dev. 0.186 0.123 0.224 0.113 0.187 0.105Prop. rel. price > 1 0.333 0.250 0.550 0.283 0.460 0.260

N 60 60 60 60 50 50

6 balls rounds

Mean rel. price 0.950 0.953 1.117 0.958 0.958 0.932Std. dev. 0.159 0.089 0.187 0.076 0.179 0.084Prop. rel. price > 1 0.333 0.222 0.704 0.222 0.480 0.160

N 27 27 27 27 25 25

12 balls rounds

Mean rel. price 0.943 0.924 0.975 0.980 1.024 0.983Std. dev. 0.208 0.145 0.234 0.136 0.192 0.12Prop. rel. price > 1 0.333 0.273 0.424 0.333 0.440 0.360

N 33 33 33 33 25 25Note: rel. price are defined as auction prices normalized with respect to the expected value of the risky asset giventhe aggregate signal. Prop. rel. price > 1 is the proportion of auctions where relative prices are greater than 1. Thisproportion measures the way subjects fell prey to the winner’s curse.

Table 4: P-values of (two-sided) pairwise comparisons of equilibrium prices in private information auctionsin different treatments

Median prices† Variances‡

CT Private MB Private CT Private MB Private

SA Private 0.023 0.236 0.077 0.863CT Private 0.249 0.142

6 balls rounds

SA Private 0.002 0.905 0.334 0.270CT Private 0.006 0.880

12 balls rounds

SA Private 0.658 0.104 0.377 0.680CT Private 0.307 0.172† Wilcoxon rank sum test. ‡ Fligner-Killeen test. Statistical significant (at the 10%) differences are bold-faced.

35

Table 5: Normalized HH indices statistics for all treatments

SA treatment CT treatment MB treatment

Private Public Private Public Private Public

Mean 0.710 0.720 0.681 0.616 0.719 0.730Std. dev. 0.215 0.233 0.168 0.188 0.183 0.175N 60 60 60 60 50 50

6 balls rounds

Mean 0.705 0.725 0.717 0.579 0.731 0.788Std. dev. 0.228 0.267 0.172 0.199 0.206 0.19N 27 27 27 27 25 25

12 balls rounds

Mean 0.715 0.716 0.651 0.647 0.707 0.672Std. dev. 0.207 0.205 0.161 0.176 0.161 0.141N 33 33 33 33 25 25

Note: Because of the restrictions related to the number of subjects and to the maximal number to bid for in ourexperiment, we use a normalized HH index defined as follows

H =(∑n

i=1( xi10∗n )2)−Hmin,n

Hmax,n −Hmin,n

where, n is the number of bidders (thus 10 ∗ n is the number of units allocated), and xi is the allocation of bidderi. Hmin,n and Hmax,n are the minimum and maximum values of the HH index given the number n of bidders in theauction and the range of possible allocations.

36

Tab

le6:

Estim

ationof

aggregatedeman

dfunction

sin

alltreatments

SA

auct

ions

CT

auct

ions

MB

auct

ions

pri

vate

public

∆pri

vate

public

∆pri

vate

public

∆(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Intercept

-21.87

5-9.589

-18.95

1-15.31

9-4

1.44

9-3

1.11

2(0.328

)(0.685

)(0.248

)(0.283

)(0.000

)(0.000

)Qua

ntity

-0.3

15-0

.280

0.03

5-0

.425

-0.3

760.

049

-0.1

76-0

.163

0.01

3(x)

(0.000

)(0.000

)(0.325

)(0.000)

(0.000

)(0.093

)(0.000

)(0.000)

(0.674

)Exp

Priv

0.72

30.

118

-0.6

150.

522

0.06

4-0

.440

0.44

20.01

19-0

.402

(E(v

t|sit

))(0.000

)(0.006

)(0.000

)(0.000)

(0.065

)(0.000

)(0.000

)(0.788)

(0.000

)Exp

Pub

0.48

80.

486

0.60

90.

598

0.51

40.

504

(E(v

t|St))

(0.000

)(0.000

)(0.000

)(0.000

)(0.000

)(0.000

)Exp

IAM

0.24

30.01

0-0

.215

0.20

60.

074

-0.1

40(E

(vt|S

IA

Mt

))(0.000

)(0.735

)(0.000

)(0.039

)(0.086

)(0.012

)Wealth

2.57

81.19

8-1

.940

6.90

85.

823

0.44

36.

096

4.67

10.02

84(ln

(Wit

))(0.013

)(0.280

)(0.042

)(0.000)

(0.000

)(0.568

)(0.000

)(0.000)

(0.958

)Net

posA

0.15

20.04

4-0

.104

(Ait)

(0.000

)(0.217

)(0.019

)Nb.

Part

1.52

31.89

40.27

9-2.021

-1.068

0.66

51.

815

1.97

10.31

7(n

t)(0.575

)(0.509

)(0.748

)(0.325)

(0.548

)(0.368

)(0.000

)(0.000)

(0.367

)

OverallR

20.28

20.23

30.25

60.29

90.48

00.39

60.24

40.29

60.26

8N

observations

1840

1840

3680

1840

1840

3680

1408

1408

2816

Nsubjects

4646

4646

4646

3838

38

Not

e:Mod

elis

estimated

foreach

treatm

ent.

Exp

Priv,

Exp

Pub

andExp

IAM

aretheexpe

cted

valuegiventheprivatesign

al,the

public

sign

alan

dthesign

altran

smittedby

the

IAM,respectively.Thislatter

isequa

lto

theaggregatean

noun

cedsign

alin

theChe

aptalk

treatm

ent,

andthelast

tran

sactionpricein

themarketba

sedtreatm

ent.

Wecontrolfor

theim

pact

ofwealthan

dthenu

mbe

rof

participan

tsin

auctionon

theaggregatebidd

ingfunction

.forMB

auctions,w

ealso

controlfor

thene

tpo

sition

intheassetA.the

∆columns

displaythemargina

limpa

ctof

enha

ncingthequ

alityof

inform

ationby

movingfrom

privateto

public

inform

ationau

ctions.Weusethefollo

wingmod

elto

derive

theseresults:

pit

=β

1+β

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+β

4E

(vt|s

it)

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t+β

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IA

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)+β

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IA

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+β

9ln

(Wit

)+β

10ln

(Wit

)Pt

+β

11A

it+β

12A

itP t

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13n

t+β

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tP t

+ε i

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whe

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ctions

and

1forpu

blic

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aredisplayedin

column

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arein

parenthe

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ignifican

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level)

estimatorsarebo

ld-faced

.

37

Table 7: Twelve versus six balls estimated aggregate demand functions in all treatments

SA auctions CT auctions MB auctions

private public private public private public(1) (2) (3) (4) (5) (6)

Intercept (6) γ1 -33.513 -6.504 -16.844 -7.559 -40.883 -24.695(0.111) (0.782) (0.347) (0.648) (0.000) (0.000)

∆ Intercept (12) γ2 19.243 -5.967 6.410 -3.553 -11.533 -8.152(0.153) (0.678) (0.587) (0.749) (0.201) (0.360)

Quantity (6) γ3 -0.266 -0.230 -0.401 -0.333 -0.161 -0.151(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

∆ Quantity (12) γ4 0.090 0.091 -0.043 -0.078 -0.029 -0.022(0.056) (0.070) (0.303) (0.050) (0.499) (0.616)

Exp Priv (6) γ5 0.937 0.549 0.455(0.000) (0.000) (0.000)

∆ Exp Priv (12) γ6 -0.331 -0.081 -0.002(0.000) (0.140) (0.979)

Exp Pub (6) γ7 0.686 0.625 0.492(0.000) (0.000) (0.000)

∆ Exp Pub (12) γ8 -0.215 -0.019 0.093(0.000) (0.713) (0.093)

Exp IAM (6) γ9 0.192 -0.023 0.214 0.113(0.000) (0.599) (0.000) (0.062)

∆ Exp IAM (12) γ10 0.075 0.026 -0.023 -0.104(0.227) (0.659) (0.785) (0.281)

Wealth (6) γ11 3.239 1.434 5.000 5.272 5.507 4.456(0.009) (0.281) (0.000) (0.000) (0.000) (0.000)

∆ Wealth (12) γ12 -1.401 0.138 2.536 0.550 2.531 0.753(0.285) (0.922) (0.033) (0.626) (0.003) (0.386)

Net pos A (6) γ13 0.133 0.139(0.007) (0.003)

∆ Net pos A (12) γ14 0.238 -0.154(0.666) (0.011)

Nb. Part (6) γ15 0.996 0.624 -0.775 -1.368 2.119 1.063(0.686) (0.806) (0.717) (0.487) (0.000) (0.065)

∆ Nb. Part (12) γ16 1.010 2.476 -2.493 0.430 -0.493 0.847(0.391) (0.054) (0.032) (0.697) (0.419) (0.172)

Overall R2 0.291 0.233 0.316 0.486 0.250 0.309N of observations 1840 1840 1840 1840 1408 1408N of subjects 46 46 46 46 38 38

Note: For each treatment and for both private and public information auctions we estimate the following modelpit = γ1 + γ2Bt + γ3x+ γ4xBt + γ5E(vt|sit) + γ6E(vt|sit)Bt + γ7E(vt|St) + γ8E(vt|St)Bt + γ9E(vt|SIAM

t )

+ γ10E(vt|SIAMt )Bt + γ11ln(Wit) + γ12ln(Wit)Bt + γ13Ait + γ14AitBt + γ15nt + γ16ntBt + εit

where Bt is a dummy variable equal to 0 for six balls auctions and 1 for 12 balls auctions. This allows to measurethe impact of enhancing the quality of the available information by increasing the precision of both private andpublic signals, moving from six to twelve balls signals. Exp Priv, Exp Pub and Exp IAM are the expected valuegiven the private signal, the public signal and the signal transmitted by the IAM, respectively. This latter is equalto the aggregate announced signal in the Cheap talk treatment, and the last transaction price in the market basedtreatment. We control for the impact of wealth and the number of participants in auction on the aggregate biddingfunction. For MB auctions, we also control for the net position in the asset A. p-values are in parentheses.Statisticalsignificant (at the 10% level) estimators are bold-faced.

38

Table 8: Inter-treatment comparison of estimated inverse demand functions in public and privateinformation treatments

Private information auctions public information auctions

MB vsSA

CT vsSA

MB vsCT

MB vsSA

CT vsSA

MB vsCT

(1) (2) (3) (4) (5) (6)

∆ Intercept -9.187 15.492 -21.681 -17.873 -4.489 -16.938(0.679) (0.575) (0.244) (0.436) (0.870) (0.325)

∆ Quantity 0.139 -0.110 0.249 0.117 -0.096 0.213(x) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000)∆ Exp Priv -0.281 -0.201 -0.080 -0.106 -0.539(E(vt|sit)) (0.000) (0.000) (0.051) (0.110) (0.332)∆ Exp Pub 0.255 0.121 -0.125(E(vt|St)) (0.608) (0.003) (0.000)∆ Exp IAM 0.207 0.242 -0.035 0.075 0.011 0.067(E(vt|SIAM

t )) (0.000) (0.000) (0.502) (0.145) (0.763) (0.206)∆ Wealth 3.553 4.276 -0.829 3.519 4.503 -1.036(ln(Wit)) (0.002) (0.001) (0.407) (0.004) (0.001) (0.285)∆ Net pos A 0.152 0.153 0.044 0.050(Ait) (0.000) (0.000) (0.300) (0.117)∆ Nb. Part 0.247 -3.553 3.727 -0.039 -2.954 2.910(nt) (0.926) (0.298) (0.102) (0.989) (0.383) (0.167)

Overall R2 0.278 0.289 0.285 0.259 0.341 0.417N of observations 3248 3680 3248 3248 3680 3248N of subjects 84 92 84 84 92 84

Note: In order to measure the impact of IAM introduction on bidders’ strategies, we estimate the following model:pit = η1 + η2Dt + η3x+ η4xDt + η5E(vt|sit) + η6E(vt|sit)Dt + η7E(vt|St) + η8E(vt|St)Dt + η9E(vt|SIAM

t )

+ η10E(vt|SIAMt )Dt + η11ln(Wit) + η12ln(Wit)Dt + η13Ait + η14nt + η15ntDt + εit

where dummy variable Dt is equal to: (1) 0 for SA auctions and 1 for MB auctions (columns 1 and 4), (2) 0 for SAauctions and 1 for CT auctions (columns 2 and 5), and (3) 0 for CT auctions and 1 for MB auctions (columns 3 and6). In the table, we display the dummy variable coefficients. The model is estimated separately for private and publicinformation auctions. Columns 3 and 6 measure the way subjects’ strategies vary with different IAMs. Exp Priv,Exp Pub and Exp IAM are the expected value given the private signal, the public signal and the signal transmittedby the IAM, respectively. This latter is equal to the aggregate announced signal in the Cheap talk treatment, andthe last transaction price in the market based treatment. We control for the impact of wealth and the number ofparticipants in auctions on the aggregate bidding function. For MB auctions, we also control for the net position inthe asset A. P-values are in parentheses. Statistically significant (at the 10% level) estimators are bold-faced.

39

Figure 1: Timing of the game for different environments. Stage 2 is played only by agents in IAMtreatments

Stage 2IAM if it exists

Stage 3Uniform-price

Stage 1Rules of the

Stage 4Symmetric i f i

Stage 5Auction

auctiongame information auction

outcomes

Agents learn their

Agents participate

End of the first stage Agents

Agents bid their

For each auction, bids are An aggregate

signal islearn their private signals and the rules of

participate in the IAM (cheap talk or market based)

stage. Agents gather information from the IAM and endeavor to

bid their demand function using their

aggregated, the stop-out price and the allocation rule are set. Both

signal is announced and agents are invited to bid again using thisrules of

the gamebased) and endeavor to

exploit it in their bidding strategies

their signals outcomes are

observed by agents but only one is applied after being

again using this more accurate signal

randomly chosen.

Figure 2: Informativeness of cheap talk games

Figure 3: Informativeness of Market-based IAM

40