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Intervention with Private Information,Imperfect Monitoring and Costly Communication

Luca Canzian, Member, IEEE, Yuanzhang Xiao, William Zame, Michele Zorzi, Fellow, IEEE, Mihaela van derSchaar, Fellow, IEEE

Abstract—This paper studies the interaction between a designerand a group of strategic and self-interested users who possessinformation the designer does not have. Because the users arestrategic and self-interested, they will act to their own advantage,which will often be different from the interest of the designer, evenif the latter is benevolent and seeks to maximize (some measureof) social welfare. In the settings we consider, the designer andthe users can communicate (perhaps with noise), the designer canobserve the actions of the users (perhaps with error) and thedesigner can commit to (plans of) actions – interventions – of itsown. The designer’s problem is to construct and implement amechanism that provides incentives for the users to communicateand act in such a way as to further the interest of the designer– despite the fact that they are strategic and self-interested andpossess private information. To address the designer’s problemwe propose a general and flexible framework that applies tomany scenarios. To illustrate the usefulness of this framework, wediscuss some simple examples, leaving further applications to otherpapers. In an important class of environments, we find conditionsunder which the designer can obtain its benchmark optimum –the utility that could be obtained if it had all information andcould command the actions of the users – and conditions underwhich it cannot. More broadly we are able to characterize thesolution to the designer’s problem, even when it does not yieldthe benchmark optimum. Because the optimal mechanism may bedifficult to construct and implement, we also propose a simplerand more readily implemented mechanism that, while falling shortof the optimum, still yields the designer a “good” result.

Index Terms—Game Theory, Incomplete Information, Mecha-nism Design, Intervention, Resource Allocation

I. INTRODUCTION

We study the interaction between a group of users anda designer. If the users are compliant or the designer cancommand the actions of the users, then the designer is facedwith an optimal control problem of the sort that is well-studied.Little changes if the users have private information (aboutthemselves or about the environment) that the designer does nothave but the designer can communicate with the users, becausethe designer can simply ask or instruct the users to reportthat information. However, a great deal changes if the users

Luca Canzian, Yuanzhang Xiao, and Mihaela van der Schaar are with theDepartment of Electrical Engineering, UCLA, Los Angeles CA 90095, USA.William Zame is with the Department of Economics, UCLA, Los Angeles CA90095, USA. Michele Zorzi is with the Department of Information Engineering,University of Padova, Via Gradenigo 6/B, 35131 Padova, Italy.

The work of Luca Canzian, Yuanzhang Xiao and Mihaela van der Schaarwas partially supported by the NSF grant CCF 1218136.

The work of Michele Zorzi was partially supported by Fondazione Cariparothrough the program “Progetti di Eccellenza 2011-2012.”

are not compliant but rather are self-interested and strategicand the designer can not command the actions and reportsof the users. In that case, the users may (and usually will)take actions and/or provide reports that are in their own self-interest but not necessarily in the interest of the designer. Theobjective of this work is to understand the extent to which thedesigner can provide incentives to the users to take actions andprovide reports that further the objectives of the designer, bethose selfish or benevolent. (The case of a benevolent designeris probably the one of most interest, but the problem facedby a benevolent designer is no easier than the problem facedby a selfish designer: the goal of a benevolent designer isto maximize some measure of social welfare – which mightinclude both total utility and some measure of fairness – but thegoal of an individual user is to maximize its own utility; hencethe incentives of the designer and of the individual user are nomore aligned when the designer is benevolent than when thedesigner is selfish, so the same incentives to misrepresent andmisbehave are present in both circumstances. Such incentivesfrequently lead to the over-use of resources and to substantialinefficiencies [1], [2].) Here, we are specifically interested insettings in which the users can send reports to the designerand the designer in turn can send messages to the users beforethe users act, after which the designer may take actions of itsown – interventions. Our use of intervention builds on [3]–[6],but we go beyond that work in considering private information,imperfect monitoring and costly communication – in additionto intervention itself.

Our work has something in common with the economictheory of mechanism design in the tradition of [7]–[11]. Indeed,our general framework builds on that of [12], and the abstracttheory of mechanism design – in particular the revelationprinciple – does play a role. However, [12] does not solve anyof our problems because after we use the revelation principle torestrict our attention to incentive compatible direct mechanismswe must still construct the optimal mechanism, which is anon-trivial undertaking.1 Moreover, when we admit physical(and other) constraints, noisy communication and imperfectmonitoring, the revelation principle does not help because

1Proposition 1 in [12] shows that the problem of choosing the optimalincentive compatible direct mechanism is a linear programming problemprovided that type sets and action sets are finite and fixed and that the designercan send arbitrary messages – but in our context the action sets may not befinite, the action set of the designer is definitely not fixed, and the designer’schoice of messages may be constrained, so our problem is different, and muchmore complicated.

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it entirely obscures all of these complications. Finally, therevelation principle simply does not hold when communicationis costly.

We treat settings in which the users have private informationbut (perhaps limited and imperfect) communication betweenthe users and the designer – more precisely, the device em-ployed by the designer – is possible. The users have theopportunity to send reports about their private information,and the device can in turn send messages to the users; inboth cases, we allow for the possibility that communicationis noisy so that the report/message sent is not necessarily thereport/message received. After this exchange of information,the users take actions. Finally, the device, having (perhapsimperfectly) observed these actions, also has the opportunityto act. Generalizing a construction of [12], we formalize thissetting as a communication mechanism. The device the designeremploys plays two roles: first, to coordinate the actions of theusers before they take them, and second, to discipline the usersafterwards. Because users are self-interested and strategic, theirreports and actions will only serve the interest of the designerif they also serve their own interests. Thus we are interestedin strategy profiles for the users that each user finds optimal,given the available information, the strategies of others and thenature of the given device; we refer to these as communicationequilibria. Note that the device is not strategic – it is a deviceafter all – but the designer behaves strategically in choosing thedevice. Because we focus here on the problem of the designer,we are interested in finding devices that support equilibria thatthe designer finds optimal. (If the designer is benevolent –i.e., intends to maximize social welfare, perhaps constrainedby some notion of fairness – these devices will also servethe interests of the users as a whole, but if the designer isself-interested they may not.) We are particularly interested inknowing when the designer can find a device so as to achievehis benchmark optimum – the outcome he could achieve if heknew all relevant information and users were fully compliant –despite the fact that information is in fact private and usersare in fact self-interested. For a class of environments thatincludes many engineering problems of interest (e.g., powercontrol [6], [13], medium access control (MAC) [4], [14], andflow control [14]–[18]) we find conditions under which thereexist mechanisms that achieve the benchmark optimum andconditions under which such mechanisms do not exist. In casethey do not exist, we find conditions such that the problemof finding an optimal protocol can be decoupled. Because theoptimal protocol may still be difficult to compute, we alsoprovide a simple algorithm that converges to a protocol that,although perhaps not optimal, still yields a “good” outcome forthe designer. [19] demonstrates that these non-optimal protocolsare very useful in a flow control management system.

Throughout, we assume that the designer can commit toa choice of a device that is pre-programmed to carry outa particular plan of action after the reports and actions ofthe users. In mechanical terms, such commitment is possibleprecisely because the designer deploys a device – hardware

or software or both – and then leaves. Indeed, the desire ofthe designer to commit is one reason that it employs a device.Although other assumptions are possible, this assumption seemsmost appropriate for the settings we have in mind, in which thedesigner is a long-lived and experienced entity who has learnedthe relevant parameters (user utilities and distribution of usertypes) over time, but the users are short-lived, come and go butdo not interact repeatedly: in a particular session they are notplaying a repeated game and are not forward-looking.2

There is by now a substantial communication engineeringliterature that addresses the problem of providing incentivesfor strategic users to obey a particular resource allocationscheme. Such incentives might be provided in a number ofdifferent ways. [3]–[6] provide incentives via intervention, andthe frameworks adopted in [15] and [20] capture the conceptof intervention as well. However, none of the preceding workshas considered the strategic aspect associated to the informationacquisition, which is the qualifying point of our analysis.In this work we extend the intervention framework to dealwith situations in which the users have private informationand try to exploit such advantage, and we propose a novelmethodology to retrieve the private information providing theusers with an incentive to declare this information truthfully.A rather different literature, including [21]–[24], adopts literalpricing schemes in which users are required to make monetarypayments for resource usage.3 Literal pricing schemes requirethe designer to have specific knowledge (the value of moneyto the users) and require a technology for making monetarytransfers, which is missing in many settings, such as wirelesscommunication. Moreover, it does not necessarily solve theproblem of a benevolent designer since monetary paymentsare by definition costly for the user making them and hencewasteful.4 An additional difficulty in employing literal paymentschemes is that it is debatable whether users would agree to apricing scheme that dynamically varies with the state of thesystem, in particular if users have to pay for a service thathad hitherto been free. A smaller literature [27]–[29] addressesenvironments in which users have private information – theirprivate monetary valuations for access to the resource – anduses ideas from mechanism design and auction theory [30]to create protocols in which users are asked to report theirprivate monetary valuations, after which access to the resourceis apportioned and users make monetary payments according

2If the interaction between the designer and the users is long and sustained,then the interaction should be modeled as a repeated game, in which case theanalysis would be completely different and the designer should consider onlypolicies which are part of a subgame perfect equilbrium.

3A different line of work, which includes [13], [25], [26] but is quite farfrom the work here, uses pricing in scenarios where users are compliant, ratherthan self-interested and strategic. In those scenarios, however, the function ofpricing is decentralization: prices induce utility functions for the users that leadthem to take the desired actions without the need for centralized control. Inthese scenarios pricing is figurative rather than literal: monetary payments arenot actually required.

4A possible exception occurs when/if all users value money in the same wayand it is possible to make transfers among users, so that some users makepayments and others receive payments.

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to their access and the reports of valuations. For very detailedcomparison of intervention, pricing, and other approaches, see[31].

The remainder of this paper is organized as follows. SectionII introduces our framework of devices and mechanisms andthe notion of equilibrium. Section III presents an example toillustrate how private information, information revelation andintervention all matter. Section IV asks when some devicesachieve the benchmark optimum. Section V studies the proper-ties of the optimal devices and Section VI offers a constructiveprocedure for choosing devices that are simple to compute andimplement – if not necessarily optimal. Section VII concludeswith some remarks.

II. FRAMEWORK

We consider a designer and a collection of users. Thedesigner chooses an intervention device and then leaves – thedesigner itself takes no further actions. In a single session thedevice interacts with a fixed number of users n, labeled from1 to n. We will write N = {1, . . . , n} for the set of users.We think of the users in a particular session as drawn froma pool of potential users, so users may be (and typically willbe) different in each session. We allow for the possibility thatusers are drawn from different pools – e.g., occupy differentgeographical locations or utilize different channels.

User i is characterized by an element of a set Ti of types;a user’s type encodes all relevant information about the user,which will include the user’s utility function and the influencethe user’s type has on other users and on the designer. WriteT = T1 × . . . × Tn for the set of possible type profiles.Users know their own type; users and the designer know thedistribution of user types π (a probability distribution on T ).5 Ifuser i is of type ti then π(· | ti) is the conditional distributionof types of other users. (We allow for the possibility thattypes are correlated, which might be the case, for instance, ifusers have private information about the current state of theworld and not only about themselves.) In each session, useri chooses an action from the set Ai of actions. We writeA = A1 × . . . × An for the set of possible action profilesand (ai, a−i) for the action profile in which user i choosesaction ai ∈ Ai and other users choose the action profilea−i ∈ A−i = A1× . . .×Ai−1×Ai+1 . . .×An; we use similarnotation for types, etc.

The designer is characterized by its utility function andthe set D of devices it might use. A device – which mightconsist of hardware or software or both – has four features:1) it can receive communications from users, 2) it can sendcommunications to users, 3) it can observe the actions of users,and 4) it can take actions of its own. As in [3], we interpret theactions of the device as interventions. We formalize a deviceas a tuple D = 〈(Ri), (Mi), µ,X,Φ, ε

R, εM , εA〉, where:• Ri is the set of reports that user i might send; write R =R1 × . . .×Rn for the set of report profiles;

5We usually think of the distribution π as common knowledge but this is notentirely necessary.

• Mi is the set of messages that the device might send touser i; write M = M1 × . . .×Mn for the set of messageprofiles;

• µ : R → ∆(M) is the message rule, which specifies the(perhaps random) profile of messages to be sent to theusers as a function of the reports received from all users;if r is the profile of observed reports we write µr for thecorresponding probability distribution on M , and µr(m)for the probability that the message m is chosen when theobserved report is r;6,7

• X is the set of interventions (actions) the device mighttake;

• Φ : R ×M × A → ∆(X) is the intervention rule, whichspecifies the (perhaps random) intervention the device willtake given the received reports, the transmitted messagesand the observed actions; if r are the observed reports, mthe transmitted messages and a the observed actions, wewrite Φr,m,a for the corresponding probability distributionon X;

• εR : R → ∆(R) encodes the noise in receiving reports:users send the report profile r but the designer observes arandom profile r distributed according to εRr ;

• εM : M → ∆(M) encodes the noise in receivingmessages: the device sends the message profile m but usersobserve a random profile m distributed according to εMm ;

• εA : A → ∆(A) encodes the error in monitoring actions:the users choose an action profile a but the device observesa random profile a distributed according to εAa .

The set of all conceivable devices is very large, but in practicethe designer will need to choose a device from some prescribed(perhaps small) subset D, so we assume this throughout. In thisgenerality, reports and messages could be entirely arbitrary buttypically reports will provide (perhaps incomplete) informationabout types, and messages will provide (perhaps incomplete)recommendations for actions, and we will frequently use thislanguage.

If the report spaces are singletons then reports are mean-ingless, so singleton report spaces Ri express the absence ofreporting. Similarly, a singleton message space M expresses theabsence of messaging and a singleton intervention space X ex-presses the absence of intervention. The absence of noise/errorwith regard to reports, messages or actions can be expressedby requiring that the corresponding mapping(s) be the identity;e.g, εRr is point mass at r and so r = r for all report profiles,etc. However, in any of these cases we would usually prefer toabuse notation and omit the corresponding component of thetuple that describes the device.

The utility Ui(a, t, ri, x) of user i depends on the actions aand types t of all users, the report ri chosen by user i, and theintervention x of the designer. The utility U(a, t, r,m, x) of the

6∆(B), where B is a set with cardinality b+ 1, denotes the b-unit simplex.7If the message m is always chosen given the observed report profile r, µr

is point mass at m, i.e., µr(z) = 1 if z = m, µr(z) = 0 otherwise. However,in this case we usually prefer to abuse notation and write µ(r) = m. Below,we will make similar notational abuses without further comment.

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designer depends on the actions a and types t of all users, onthe reports r, the messages m and the intervention x of thedesigner. The dependence of utility on reports and messagesallows for the fact that communication may be costly. Notethat the utility of a user depends only on the report that usersends, but the utility of the designer depends on the messagesit sends and on the reports of the users. If this seems strange,keep in mind that if the designer is benevolent and seeks tomaximize social utility, he certainly cares about the reportingcosts of users.

A communication mechanism, or mechanism for short, is atuple C = 〈N, (Ti, Ai, Ui), π, U,D〉 that specifies the set N ofusers, the sets Ti of user types, the sets Ai of user actions,the utility functions Ui of users, the distribution π of types, theutility function U of the designer, and the device D. We viewthe designer as choosing the device, which is pre-programmed,but otherwise taking no part: the users choose and execute plansand the device carries out its programming.

The operation of a communication mechanism C is as fol-lows.• users make reports to the device;• the device “reads” the reports (perhaps with error) and

sends messages to the users (perhaps depending on therealization of the random rule);

• users “read” the messages8 (perhaps with error) and takeactions;

• the device “monitors” the actions of the users (perhapsimperfectly) and, following the rule, makes an intervention(perhaps depending on the realization of the random rule).

A strategy for user i is a pair of functions fi : Ti → Ri, gi :Ti ×Mi → Ai that specify which report to make, conditionalon the type of user i, and which action to take, conditional onthe type of user i and the message observed. We do not specifya strategy for the device because the device is not strategic,its behavior is completely specified by the message rule andthe intervention rule – but the designer behaves strategically inchoosing the device. Given a profile (f, g) of user strategies,and the intervention device D, the expected utility of a useri whose type is ti is obtained by averaging over all randomvariables involved, i.e.,9:

EUi(f, g, ti, D) =∑

t−i∈T−i

π(t | ti)∑r∈R

εRr (r)∑m∈M

µr(m)·

·∑m∈M

εMm (m)∑a∈A

εAa (a)∑x∈X

Φr,m,a(x)Ui(a, t, ri, x)

where rj = fj(tj) and aj = gj(tj , mj), ∀ j ∈ N , are the reportssent and the actions taken by users. Similarly, the expected

8Note that we assume that each user i can only read its own message mi.However, our framework is suitable to model also situations in which user i isable to hear the message mj intended for user j. In this case it is sufficient tofocus on devices in which the message sent to user j is part of the messagesent to user i.

9We have tacitly assumed that all the probability distributions under con-sideration have finite or countably infinite support – which will certainly bethe case if the spaces under consideration are themselves finite or countablyinfinite; in a more general context we would need to replace summations byintegrals and to be careful about measurability.

utility of the designer is

EU(f, g,D) =∑t∈T

π(t)∑r∈R

εRr (r)∑m∈M

µr(m)·

·∑m∈M

εMm (m)∑a∈A

εAa (a)∑x∈X

Φr,m,a(x)U(a, t, r,m, x)

The strategy profile (f, g) is an equilibrium if each user isoptimizing given the strategies of other users and the device D;that is, for each user i we have

EUi(fi, f−i, gi, g−i, ti, D) ≥ EUi(f ′i , f−i, g′i, g−i, ti, D) (1)

for all strategies f ′i : Ti → Ri, g′i : Ti × Mi → Ai.10

We often say that the device D sustains the profile (f, g).We remark that the existence of such an equilibrium is notalways guaranteed without additional assumptions and needs tobe explicitly addressed in the specific case at hand.

The designer seeks to optimize his own utility by choosing adevice D from some prescribed class D of physically feasibledevices. Because users are strategic, the designer must assumethat, whatever device D is chosen, the users will follow someequilibrium strategy profile (f, g). Since the designer willtypically recommend actions, we assume that, if more than oneequilibrium strategy profile exists, the users choose (becausethey are coordinated to) the equilibrium that the designer mostprefers (in case of a benevolent manager, it usually coincideswith the equilibrium that the users prefer). Hence, the designerhas to solve the following Optimal Device (OD) problem11:

argmaxD∈D

maxf,g

EU(f, g,D)

subject to:EUi(fi, f−i, gi, g−i, ti, D) ≥ EUi(f ′i , f−i, g′i, g−i, ti, D)

∀ i ∈ N , ∀ ti ∈ Ti , ∀ f ′i : Ti → Ri , ∀ g′i : Ti ×Mi → Ai

We say that a solution D of the above problem is an optimaldevice. To maintain parallelism with some other literature, wesometimes abuse language and refer to the designer’s problemas choosing an optimal mechanism – even though the designeronly chooses the device and not the types of users, their utilities,etc. Note that optimality is relative to the prescribed set D ofconsidered devices. Moreover, the expected utility the designerobtains choosing the optimal device must not be confusedwith the benchmark optimum utility the designer could achieveif users were compliant, which is in general higher. If theycoincide, we say that the device D is a maximum efficiencydevice.

10The notion of equilibrium defined here is that of a Bayesian Nashequilibrium of the Bayesian game induced by the communication mechanism.For simplicity, we have restricted our attention to equilibrium in pure strategies;we could also allow for equilibria in mixed strategies [32].

11Because the utility functions of the users depend on reports, and the utilityfunction of the designer depends on messages and reports, which are parametersof the device chosen, this tacitly assumes that utility functions are defined on adomain sufficiently large to encompass all the possibilities that may arise whenany device D ∈ D is chosen.

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A. Null reports, messages and interventions

In many (perhaps most) concrete settings, it is natural topresume that users might sometimes choose not to make reportsand that the device might sometimes not send messages ormake an intervention. The easiest way to allow for thesepossibilities is simply to assume the existence of null reports,null messages and null actions. In particular, we can assumethat for each user i there is a distinguished report r∗i whichis to be interpreted as “not sending a report”. (On the deviceside, observing r∗i should be interpreted as “not receiving areport”.) Because not making a report should be costless, weshould assume that, fixing types, reports of others to the device,actions by the users and intervention by the device, r∗i yieldsutility at least as great as any other report: Ui(a, t, r∗i , x) ≥Ui(a, t, ri, x) and U(a, t, r∗i , r−i,m, x) ≥ U(a, t, ri, r−i,m, x),for all i, a, t, x, ri, r−i,m. Given this assumption, and usingutility when sending the report r∗i as the baseline, we caninterpret the differences Ui(a, t, r

∗i , x) − Ui(a, t, ri, x) and

U(a, t, r∗i , r−i,m, x)−U(a, t, ri, r−i,m, x) as the cost to useri and to the designer, respectively, of sending the report ri.In this generality, the cost of sending a report might dependon all other variables. We remark that this cost does not takeinto consideration the impact of the communication on theinteraction among the users and the intervention device: indeciding whether or not to send a report, a user must take intoaccount the fact that sending a report may alter the messagessent by the device and hence the actions of the users and theintervention of the device. So sending a report, while increasingthe instantaneous communication cost, may still lead to a higherutility because it influences the strategic choices of others.

Similarly, we could assume that for each user i there is adistinguished message m∗i that the device might send but whichwe interpret as “not sending a message”. (On the user side, weinterpret receipt of the message m∗i as “not receiving a mes-sage”.) Because not sending a message m∗i should be costless,we assume that U(a, t, r,m∗i ,m−i, x) ≥ U(a, t, r,mi,m−i, x)for all i, a, t, r,m−i, x,mi, and so interpret the differenceU(a, t, r,m∗i ,m−i, x) − U(a, t, r,mi,m−i, x) as the cost ofsending the message mi, which might depend on all othervariables.

Finally, we could assume that there is a distinguished in-tervention x∗ that we interpret as “not making an interven-tion”. If (as we usually do) we want to interpret an inter-vention as a punishment, we should assume that x∗ yieldsutility at least as great as any other intervention for eachuser and the designer: Ui(a, t, ri, x∗) ≥ Ui(a, t, ri, x) andU(a, t, r,m, x∗) ≥ U(a, t, r,m, x) for all i, a, t, r,m, x, andwe interpret the differences Ui(a, t, ri, x∗)−Ui(a, t, ri, x) andU(a, t, r,m, x∗)−U(a, t, r,m, x) as the cost of the interventionto user i and to the designer, respectively, which might dependon all other variables.

If the sets of reports (respectively, messages, interventions)are singletons, then by default there are no possible reports(respectively, messages, interventions).

If D is a device for which “not making an intervention”

is possible and (f, g) is an equilibrium with the property thatΦr,m,a(x∗) = 1, for all type profiles t, observed reports r,sent messages m and observed actions a (with r, m and aoccurring with positive probability), we say that D sustains(f, g) without intervention. The most straightforward interpreta-tion is that the device threatens punishments for deviating fromthe recommended actions and that the threats are sufficientlysevere that they do not need to be executed. Again, this isnatural in context: by using the intervention device, the designercommits to meting out punishments for deviation, even if thosepunishments are costly for the designer as well as for the users.

B. Direct mechanisms

To be consistent with [12], we say that the mechanism Cd isa direct mechanism if Ri = Ti for all i (users report theirtypes, not necessarily truthfully) and M = A (the devicerecommends action profiles), there are no errors, and reportsand messages are costless (i.e., utility does not depend onreports or messages). If Cd is a direct mechanism we write(f∗, g∗) = (f∗1 , . . . , f

∗n, g∗1 , . . . g

∗n) for the strategy profile in

which users are honest (report their true types) and obedient(follow the recommendations of the device); that is, f∗i (ti) = tiand g∗i (ti, ai) = ai for every user i, type ti, and recommenda-tion ai = µi(ti). If (f∗, g∗) is an equilibrium, we say that Cdis incentive compatible. If a device is such that the resultingmechanism is an incentive compatible direct mechanism, wesay that the device is incentive compatible.

Incentive compatible direct mechanisms play a special rolebecause of the following generalization of the revelation princi-ple. (We omit the proof, which is almost identical to the proofof Proposition 2 in [12].)

Proposition 1. If C is a mechanism for which reports andmessages are costless and (f, g) is an equilibrium of themechanism C, then there is an incentive compatible directmechanism Cd with the same action and intervention spaces forwhich the honest and obedient strategy profile (f∗, g∗) yieldsthe same probability distribution over outcomes as the profile(f, g).

As we shall see later, (this version of) the revelation principleis useful but its usefulness is limited for a number of reasons.The first reason is that, although it restricts the class ofmechanisms over which we must search to find the designer’smost preferred outcome, we still have to find the optimal devicein this class, which is not always an easy task. The secondreason is that in practice there will often be physical limitationson the devices that the designer can employ (because of limitsto the device’s monitoring capabilities, for instance) and hencelimitations on the communication mechanisms that should beconsidered, but these may not translate into limitations on acorresponding direct mechanism. For instance, in a flow controlscenario, it will often be the case that the device can observetotal flow but not the flow of individual users and can onlyobserve this flow with errors; no such restrictions occur in direct

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mechanisms. Finally, as noted before, the revelation principledoes not hold when communication is costly.

C. Special cases

The framework we have described is quite general so it isworth noting that many, perhaps more familiar, frameworks aresimply special cases:• If T , R, M and X are all singletons, then our framework

reduces to an ordinary game in normal form and ourequilibrium notion reduces to Nash equilibrium.

• If R, M and X are all singletons, then our frameworkreduces to an ordinary Bayesian game and our equilibriumnotion reduces to Bayesian Nash equilibrium.

• If T , R and X are all singletons, then our frameworkreduces to a game with a mediation device and ourequilibrium notion reduces to correlated equilibrium [33].

• If T , R and M are all singletons, then our frameworkreduces to the intervention framework of [3] and ourequilibrium notion reduces to intervention equilibrium.

• If there are no errors, and reports and messages arecostless, then our framework reduces to a communicationgame in the sense of [12] and our equilibrium notionreduces to communication equilibrium.

III. WHY INTERVENTION AND INFORMATION REVELATIONMATTER

To illustrate our framework, we give a simple example toshow that strategic behavior matters, intervention matters, andcommunication plus intervention matters – in the sense that theyall change the outcomes that can be achieved.

We consider the problem of access to two channels A andB (e.g., two different bandwidths, or two different time slots).In each session, two users (identified as user 1 and user 2, butdrawn from the same pool of users) can access either or bothchannels; we use A,B,AB to represent the obvious actions.Each user seeks to maximize its utility, which is the sum of itsown goodput in the two channels.

Potential users are of four types: HL, ML, LM and LH;the probability that a user is of a given type is 1/4. We interpreta user’s type xy as the quality of channels A,B to that user:channel A has quality x (Low, Medium or High), channel Bhas quality y (Low, Medium or High).12 The goodput obtainedby user i = 1, 2 from a given channel depends on the user’stype and on which user(s) access the channel.• if user i does not access the channel it obtains goodput

= 0• if both users access the channel they interfere with each

other and both users obtain goodput = uI• if user i is the only user to access channel A and its type

is xy then it obtains goodput ux (where x = L,M,H)

12Note that the quality to a user is correlated across channels: each userfinds one channel to be of Low quality and the other to be of Medium orHigh quality. This is not at all essential – the qualitative comparisons would beunchanged if we assumed quality to a user was uncorrelated across channels –but the calculation would be much messier.

• if user i is the only user to access channel B and its typeis xy then it obtains goodput uy (where y = L,M,H)

We assume 2uI < uL < uM < uH .We consider five scenarios: (I) no intervention or communica-

tion, (II) communication but no intervention, (III) interventionbut no communication, (IV) intervention and communication,and (V) the benchmark setting in which the designer has perfectinformation and users are obedient. For simplicity, we assumethat the devices available to the designer are very restricted:reports and messages are costless, there are no errors and theactions are either x∗ = “take no action” or x1 = “access bothchannels”. If the device takes no action, user utilities are asabove; if the device accesses both channels then each user’sgoodput is uI on each channel the user accesses.13 The designeris benevolent and hence seeks to maximize social utility – theexpected sum of user utilities.

I No communication, No Intervention Independently ofthe user’s type, the other user’s type, and the other user’s action,it is always strictly better for each user to access both channels,so in the unique (Bayesian Nash) equilibrium both users alwayschoose action AB , and (in obvious and suggestive notation),(expected) social utility is EU(I) = 4uI .

II Communication, No Intervention Nothing changes fromscenario I: no matter what the users report and the devicerecommends, it is strictly better for each user to access bothchannels, so in the unique equilibrium both users always chooseaction AB , and social utility is EU(II) = 4uI .

III Intervention, No Communication The sets Ri of reportsand M of messages are singletons, so the device obtains noinformation about the users and can suggest no actions to theusers. The best the designer can do is to use an interventionrule that coordinates the two users to different resources; giventhe restriction on device actions an optimal rule is:

Φ (a1, a2) =

{x∗ if a1 = A and a2 = Bx1 otherwise

where a1 and a2 are the actions adopted by the two users,which are assumed to be aware of the intervention rule. Giventhis intervention rule, the best equilibrium strategy profile (i.e.,the one that yields highest social utility) is for user 1 to accesschannel A and user 2 to access channel B, so that there isnever a conflict.14 Given the distribution of types, social utilityis EU(III) = (uH/2) + (uM/2) + uL.

IV Communication, Intervention We consider a directmechanism in which the users report their types (Ri = Ti)

13Note that in this model the utility obtained when accessing a channel inthe presence of interference does not depend on the number of interfererspresent and on their channel qualities, which may not be realistic in certainscenarios. This assumption is made here in order to keep the discussion simple,but could be easily relaxed at the price of a much more cumbersome discussionin terms of notation and number of cases to be considered. In addition, in mostreasonable scenarios (i.e., when the goodput obtained in the presence of anyamount of interference is significantly lower than that obtained in its absence),the qualitative conclusions we draw here would be maintained.

14This is not the only equilibrium but it is the best, both for the designerand for the users. In the other equilibrium the users access both channels.

7

and the device D recommends actions (M = A). The deviceuses the following message and intervention rules:

µ(r1, r2) =

(A,B) if r1 = HL or r1 = MLor r2 = LH or r2 = LM

(B,A) otherwise

Φ(r1, r2, a1, a2) =

{x∗ if (a1, a2) = µ(r1, r2)x1 otherwise

where r1, r2 are the reports and a1, a2 are the actions. Thisis an incentive compatible direct mechanism. To see this wemust show that the honest and obedient strategy (f∗1 , g

∗1) is the

most preferred strategy for all types of user 1, given that user 2follows its honest and obedient strategy (f∗2 , g

∗2), and conversely

for user 2. We will describe the calculations for user 1, fromwhich those for user 2 can be derived by the symmetry of theproblem.

Assume user 1 is of type HL. If it is honest and obedient, itobtains a utility of uH because it accesses its preferred channel.This utility is always higher than the utility it obtains not beingobedient, i.e., if it does not follow the recommendation. In factin this case it never obtains a utility higher than 2uI becausethe channels are interfered by the device. Now assume user 1 isobedient but not honest. If it reports type ML it can still accessits preferred channel, obtaining a utility of uH , the same as ifit were honest. If it reports type LM or LH , it accesses halfof the time its preferred channel and half of the time its lesspreferred channel (depending on the type of user 2), obtainingan expected utility of (uH + uL)/2 which is lower than uH .These considerations translate mathematically into the set ofinequalities in Fig. 1 for EU1(f∗, g∗, HL,D), stating that user1 has an incentive to be honest and obedient if it is of typeHL. Fig. 1 also shows the analogous inequalities if user 1 isof type ML, LM or LH .

Notice that following this mechanism never leads to inter-ference (users always access different channels) and users are“assigned” to the most efficient channels 7/8 of the time.However, users are not always assigned to the most efficientchannels: if type profiles are (t1, t2) = (ML,HL) or (t1, t2) =(LH,LM) then user 1 is assigned to channel A and user 2 isassigned to channel B, which is inefficient. This inefficiency isan unavoidable consequence of incentive compatibility: if user2 were always assigned to his preferred channel A when hereported HL (for instance) then he would never be willing toreport ML when that was his true type. Expected social utilityunder this mechanism is

EU(IV ) = (3uH/4) + (3uM/4) + (uL/2)

V Benchmark Social Optimum: Public Information, Per-fect Cooperation The social optimum is obtained by assigningthe user with the best channel quality to his favorite channeland never assigning two users to the same channel. Expectedsocial utility is

EU(V ) = (7uH/8) + (5uM/8) + (uL/2)

Direct calculation shows that social utilities in four of thefive scenarios are strictly ranked:

EU(I) = EU(II) < EU(III) < EU(IV ) < EU(V )

In words: in comparison to the purely Bayesian scenario(no intervention), communication without intervention achievesnothing, intervention without communication improves socialutility by dampening destructive competition, intervention withcommunication improves social utility even more by extractingsome information and using that information to promote a moreefficient coordination across types, but even intervention withcommunication does not achieve the benchmark social optimumunder full cooperation. It is possible to show that the sameconclusions would be obtained in an environment with n usersand m channels (for arbitrary n,m), provided that m ≥ n andmuI < uL < uM < uH .

It is worth noting that similar comparisons across scenarioscould be made in many environments and the ordering ofexpected social utility would be as above:

EU(I) ≤ EU(II) ≤ EU(III) ≤ EU(IV ) ≤ EU(V )

In general, any of these inequalities might be strict.

IV. RESOURCE ALLOCATION GAMES IN COMMUNICATIONENGINEERING

In the following sections of the paper, we explore the de-signer’s problem in a class of abstract environments that exhibitsome features common to many resource sharing situations incommunication networks, including power control [6], [13],MAC, [4], [14], and flow control [14]–[18].

The contributions of this part of the paper are the following.We characterize the direct communication mechanisms thatare optimal among all mechanisms. We provide conditions onthe environment under which it is possible for the designerto achieve its benchmark optimum – the outcome it couldachieve if users were compliant – and conditions under whichit is impossible for the designer to achieve its benchmarkoptimum. Although we can characterize the optimal device,other mechanisms are also of interest, for several reasons. Theoptimal device may be very difficult to compute. It is thereforeof some interest to consider mechanisms that are sub-optimalbut easy to compute, and we provide a simple algorithm thatconverges to such a mechanism. Moreover, in some situations,it may not be possible for the users to communicate with thedesigner, so it is natural to consider intervention schemes that donot require the users to make reports. These sub-optimal devicesare very useful to implement practical schemes and, for thisreason, are used in [19] to design a flow control managementsystem robust to self-interested and strategic users.

A. The considered environment

In this subsection we formalize the particular (but, at thesame time, quite general) environment we consider from now

8

EU1(f∗, g∗, HL,D) =

uH > 2uI ≥ EU1(f1, f∗2 , g1, g

∗2 , HL,D) ∀ f1, if g1(HL, a1) 6= a1

uH = EU1(f1, f∗2 , g∗, HL,D) if f1(HL) = ML

uH > (uH + uL)/2 = EU1(f1, f∗2 , g∗, HL,D) if f1(HL) = LM orLH

EU1(f∗, g∗,ML,D) =

uM > 2uI ≥ EU1(f1, f∗2 , g1, g

∗2 ,ML,D) ∀ f1, if g1(ML, a1) 6= a1

uM = EU1(f1, f∗2 , g∗,ML,D) if f1(ML) = HL

uM > (uH + uL)/2 = EU1(f1, f∗2 , g∗,ML,D) if f1(ML) = LM orLH

EU1(f∗, g∗, LM,D) =

(uM + uL)/2 > 2uI ≥ EU1(f1, f∗2 , g1, g

∗2 , LM,D) ∀ f1, if g1(LM, a1) 6= a1

(uM + uL)/2 = EU1(f1, f∗2 , g∗, LM,D) if f1(LM) = LH

(uM + uL)/2 > uL = EU1(f1, f∗2 , g∗, LM,D) if f1(LM) = HL orML

EU1(f∗, g∗, LH,D) =

(uH + uL)/2 > 2uI ≥ EU1(f1, f∗2 , g1, g

∗2 , LH,D) ∀ f1, if g1(LH, a1) 6= a1

(uH + uL)/2 = EU1(f1, f∗2 , g∗, LH,D) if f1(LH) = LM

(uH + uL)/2 > uL = EU1(f1, f∗2 , g∗, LH,D) if f1(LH) = HL orML

Fig. 1. Set of inequalities showing that user 1 has an incentive to be honest and obedient

on, motivating each assumption with examples of its applicationin resource sharing situations in communication networks.

We consider a finite and discrete type set made by realnumbers Ti = {τi,1, τi,2, . . . , τi,vi} ⊂ R, vi ∈ N, in whichthe elements are labeled in increasing order, τi,1 < τi,2 <. . . < τi,vi . We interpret the type of a user as the valuationof a particular resource for the user (e.g., different types mayrepresent different quality of service classes). We assume thatevery type profile has a positive probability to occur, i.e.,π(t) > 0, ∀ t. We allow the users to take actions in a continuousinterval Ai =

[amini , amaxi

]⊂ R, which we interpret as the

level of resource usage (e.g., it may represent the adoptedtransmission power, which is positive and upper bounded). Weassume that the devices available to the designer are such thatreports and messages are costless, there are no errors, and thereexists the intervention action x∗ ∈ X which we interpret as “nointervention”. In this case we can simply write Ui(a, t, x) forthe utility of user i and U(a, t, x) for the utility of the designerand we can restrict our attention to incentive compatible directmechanisms. That is, we consider only the incentive compatibledevices D = 〈(Ti), (Ai), µ,X,Φ〉 in which x∗ ∈ X .

We assume that the designer’s utility satisfies the followingassumptions, ∀ t ∈ T ,A1: U(a, t, x∗) > U(a, t, x), ∀ a ∈ A, ∀X , ∀x ∈ X , x 6= x∗

A2: gM (t) = argmaxa U(a, t, x∗) is uniqueA3: gM (t) is differentiable with respect to ti and ∂gMi (t)

∂ti> 0

15

Assumption A1 states that the “no intervention” action is thestrictly preferred action of the designer, regardless of users’actions and types. Interpreting interventions as punishments,assumption A1 asserts that the designer is not happy if theusers are punished.

Assumption A2 states that, for every type profile t ∈ T ,the users’ joint action profile that maximizes the designer’s

15This assumption requires the designer’s utility to be defined over a

continuous interval that includes the finite type set T . Note that if ∂gMi (t)

∂ti< 0

it is possible to define a new type variable as the inverse of the original type,such that A3 is satisfied.

utility is unique, and by assumption A3, each component ingM is continuous and increasing in the type of that user. Ifactions represent the level of resource usage and types representresource valuations, assumption A3 asserts that the higher i’svaluation the higher i’s socially optimum level of resourceusage.

Under these assumptions, the benchmark optimum for thedesigner can be easily determined

EU ben =∑t∈T

π(t)U(gM (t), t, x∗) (2)

For each type profile t ∈ T , we define the completeinformation game

Γ0t = (N,A, {Ui(·, t, x∗)}ni=1)

Γ0t is the complete information game (users know everybody’s

type) that can be derived from our general framework assumingthat sets of types Ti, reports Ri, messages Mi and interventionsX are singletons (in particular, X = {x∗}). It can be thoughtas the game that models users’ interaction in the absence of anintervention device and when the type profile is known.

The strategy of user i in this context is represented bythe function gi : T → Ai (notice that we can omit thedependence on the messages), since the function f : T → Ris automatically defined (users do not send reports or re-ceive messages, or equivalently, always send the report “noreport” and receive the message “no message”). We denoteby gNE

0

(t) =(gNE

0

1 (t), . . . , gNE0

n (t))

a Nash Equilibrium(NE) of the game Γ0

t , which is an action profile so that eachuser obtains its maximum utility given the actions of the otherusers, i.e., ∀ i ∈ N and ∀ gi : T × {m∗} → Ai

Ui

(gNE

0

(t), t, x∗)≥ Ui

(gi(t), g

NE0

−i (t), t, x∗)

We assume that users’ utilities Ui(a, t, x∗) are twice differ-entiable16 with respect to a and, ∀ a ∈ A, ∀ t ∈ T , ∀ i, j ∈ N ,

16All the results go through if utility functions are only continuous. Theassumption that utility functions are twice differentiable is made only in orderthat submodularity (A5) takes a particularly convenient form.

9

i 6= j,A4: Ui(a, t, x

∗) is quasi-concave in ai and there ex-ists a unique best response function hBRi (a−i, t) =argmaxai Ui(a, t, x

∗)

A5: ∂2Ui(a,t,x∗)

∂ai∂aj≤ 0

A6: There exists gNE0

such that gNE0

(t) ≥ gM (t) 17 andgNE

0

k (tk, t−k) > gMk (tk, t−k) for some user k ∈ N andtype tk ∈ Tk

Since for A4 the users’ utilities are quasi concave (thusthe game Γ0

t is a quasi-concave game) and the best responsefunction hBRi (a−i, t) that maximizes Ui(a, t, x

∗) is unique,either i’s utility is monotonic with respect to ai, or it increaseswith ai until it reaches a maximum for hBRi (a−i, t), anddecreases for higher values. As a consequence, a NE gNE

0

(t)of Γ0

t exists. In fact, the best response function hBR(a, t) =(hBR1 (a−1, t), . . . , h

BRn (a−n, t)

)is a continuous function from

the convex and compact set A to A itself, therefore Brouwer’sfixed point theorem ensures that a fixed point exists.

Assumption A5 asserts that Γ0t is a submodular game and

ensures that hBRi (a−i, t) is a non increasing function of aj ,j 6= i. Interpreting ai as i’s level of resource usage, this situationreflects resource allocation games where it is in the interest ofa user not to increase its resource usage if the total level of useof the other users increases, in order to avoid an excessive useof the resource. Nevertheless, assumption A6 says that strategicusers use the resources more heavily compared to the optimal(from the designer’s point of view) usage level.

The class of games satisfying assumptions A1-A6 includesthe linearly coupled games [14] and many resource allocationgames in communication networks, such as the MAC [4], [14],power control [6], [13] and flow control [14]–[18] games,assuming that the designer’s utility is increasing in the users’utilities (i.e., a benevolent designer).

B. Intervention in the complete information setting

As a further step toward the objective of this paper whichis the design of a mechanism dealing with both informationrevelation and action enforcement, we introduce here the specialcase of intervention in the complete information setting.

For each type profile t ∈ T and intervention rule Φ : A →∆(X) (we can omit the dependence on reports and messages),we define the complete information game

Γt = (N,A, {Ui(·, t, x)}ni=1)

where x is drawn according to the distribution Φ(a), i.e., withprobability Φa(x). Γt is the complete information game (usersand designer know everybody’s type) that can be derived fromour general framework assuming that sets of types Ti, reportsRi and messages Mi are singletons. Our general frameworkreduces in this case to the intervention framework of [3] andour equilibrium notion reduces to intervention equilibrium.

17Throughout the paper, inequalities between vectors are intendedcomponent-wise.

As in the game Γ0t , the strategy of user i is represented

only by the function gi : T → Ai, but in this case i has totake into account the effect on its (expected) utility of theintervention action x, which depends on the adopted actionprofile a. According to the notions introduced in the generalframework, we say that a device D, defined by the set ofinterventions X and the intervention rule Φ, sustains (withoutintervention) the strategy profile g(t) = (g1(t), . . . , gn(t)) in Γtif g is an equilibrium of Γt (and Φg(t)(x

∗) = 1). If there existsa device D able to sustain (without intervention) the profile gin Γt, we say that g is sustainable (without intervention) in Γt.

V. OPTIMAL DEVICES

In this section we study the class of environments introducedin Section IV with the general framework proposed in SectionII. In particular, we take the part of a designer seeking tomaximize his own expected utility in the presence of self-interested and strategic users, choosing an optimal device inthe class of available devices D specified in Section IV .

First of all we wonder if the designer can choose a maximumefficiency device D ∈ D to obtain his benchmark utilitydespite the fact that the users are strategic. We characterize theexistence and the computation of maximum efficiency devicesbased on some properties of the complete information setting.Moreover, we prove that a necessary condition for the existenceof a maximum efficiency device requires the type sets to besufficiently sparse.

Even for cases in which a maximum efficiency device doesnot exist, the designer is still interested in obtaining the besthe can, choosing an optimal device. For this reason we studythe problem of finding the optimal device and we prove that,under some properties of the complete information setting, theoriginal problem can be decoupled into two sub-problems thatare easier to solve.

A. Properties of a maximum efficiency device

In this subsection we address the problem of the existenceand the computation of a maximum efficiency incentive com-patible device.

The first result we derive asserts that a maximum efficiencydevice exists if and only if, for every type profile t, the optimal(for the designer) strategy profile gM (t) is sustainable withoutintervention in Γt, and users have incentives to reveal theirreal type given that they will adopt gM and the interventiondevice does not intervene. If this is the case, we are also ableto characterize all maximum efficiency devices.

Proposition 2. D = 〈(Ti), (Ai), µ,X,Φ〉 is a maximum effi-ciency device if and only if, ∀ t ∈ T ,

1: the optimal action profile gM (t) is sustainable withoutintervention in Γt;

2: each user i having type ti prefers the action profile gM (t)with respect to the action profile gM (t′i, t−i), for every

10

alternative type t′i user i might have, i.e,∑t−i∈T−i

π(t | ti)Ui(gM (t), t, x∗

)≥

≥∑

t−i∈T−i

π(t | ti)Ui(gM (t′i, t−i), t, x

∗)∀ i ∈ N, ∀ ti ∈ Ti, ∀ t′i ∈ Ti

3: the suggested action profile is the optimal action profile ofgame Γt, i.e., µ(t) = gM (t);

4: the restriction of the intervention rule in r = t and m =gM (t), i.e., Φa = Φt,gM (t),a, sustains without interventiongM (t) in Γt.

Proof: See Appendix ACondition 1 is related to what is achievable by the designer

in the complete information setting, condition 2 is related to thestructure of the environment (which is not controllable by thedesigner), while conditions 3-4 say how to obtain a maximumefficiency direct mechanism once 1-2 are satisfied.

In the second result we combine condition 2 of Proposition2 with assumptions A3-A6 to derive a sufficient conditionon the type set structures under which a maximum efficiencyincentive compatible direct mechanism does not exist. Wedefine the bin size βk of user k’s type set, Tk, as themaximum distance between two consecutive elements of Tk:βk = maxs∈{1,...,vk−1} (τk,s+1 − τk,s). We define the binsize β as the maximum among the bin sizes of all users:β = maxk∈N βk.

Proposition 3. There exists a threshold bin size ζ > 0 so thatif β ≤ ζ then a maximum efficiency incentive compatible directmechanism does not exist.

Proof: Let k ∈ N and tk ∈ Tk be such that gNE0

k (t) >gMk (t), ∀ t−i ∈ T−i. We rewrite condition 2 of Proposition 2for user k and type tk:∑t−k∈T−k

π(t | tk)Uk(gM (tk, t−k), t, x∗

)≥

≥∑

t−k∈T−k

π(t | tk)Uk(gM (t′k, t−k), t, x∗

)(3)

∀ t′k ∈ Tk. We have hBRk (gM−k(t), t) ≥ hBRk (gNE0

−k (t), t) =

gNE0

k (t) > gMk (t), where the first inequality is valid becauseof the submodularity.

Let tk(t−k) be the value of user k’s type so thatgMk (tk(t−k), t−k) = hBRk (gM−k(tk(t−k), t−k), t) if it exists (inthis case A3 guarantees it is greater than tk); and tk(t−k) =τk,vk otherwise. Let tk = mint−k

tk(t−k). If(tk, tk

]⋂Tk 6= ∅

(in particular, this is true if β ≤ tk − tk), ∀ t′k ∈(tk, tk

]⋂Tk

and ∀ t−k ∈ T−k we obtain

Uk(gM (t′k, t−k), t, x∗

)> Uk

(gM (tk, t−k), t, x∗

)contradicting Eq. (3).

Interpretation: when user k’s type is tk, k’s resource usagethat maximizes the designer’s utility, gMk (t), is lower than the

one that maximizes k’s utility, hBRk (gM−k(t), t), ∀ t−k ∈ T−k. Ifk reports a type t′k slightly higher than tk, then the interventiondevice suggests a slightly higher resource usage, allowing kto obtain a higher utility. Hence, k has an incentive to cheatand resources are not allocated as efficiently as possible. Toavoid this situation, the intervention device might decrease theresources given to a type t′k. In this case the loss of efficiencyoccurs when the real type of k is t′k and it does not receivethe resources it would deserve. These two cases are such thatat least one of them corresponds to a non-zero inefficiency.Since both occur with positive probability, a positive overallinefficiency is unavoidable.

It is worth noting that we consider finite type sets anda finite intervention rule set mainly to simplify the logicalexposition. However, all results might be derived also withinfinite and continuous sets. In particular, if type sets arecontinuous Proposition 3 implies that a maximum efficiencyincentive compatible direct mechanism never exists.

B. Properties of an optimal device

If a maximum efficiency device exists, the set of optimaldevices in D coincides with the set of maximum efficiencydevices in D, that is characterized in Proposition 2. If amaximum efficiency device does not exists, the designer seeksto obtain the best he can, minimizing the loss of efficiency.He has to choose the optimal device solving the OD problem.However, this may be computationally hard.

In this subsection we consider some additional conditions tosimplify the OD problem. First, we assume that the designer’sutility is a function of the users’ utilities (this is the case, forexample, of a benevolent designer that seeks to maximize somemeasure of social welfare). Moreover, we suppose that, for eachtype profile t ∈ T , every action profile g(t) lower than gNE

0

(t)is sustainable without intervention in Γt. Finally, we assume thatthe utility of a user i adopting the lowest action amini is alwaysequal to 0, i.e., Ui(amini , a−i, t, x) = 0, ∀ a−i, t, x. Interpretingamini as no resource usage, this means that, independently oftypes and other users’ actions, a user that does not use resourcesobtains no utility. In particular, this last assumption implies that:

Lemma 1. The utility of user i is non increasing in the actionsof the other users.

Proof:

Ui(a, t, x) = Ui(amini , a−i, t, x) +

∫ ai

amini

∂Ui(z, a−i, t, x)

∂z∂z

=

∫ ai

amini

∂Ui(z, a, t, x)

∂z∂z

∂Ui(a, t, x)

∂aj=

∫ ai

amini

∂2Ui(z, a−i, t, x)

∂z∂aj∂z ≤ 0

where the inequality is valid because of A5.Under the additional assumptions of this subsection, we can

prove the following result that allows the designer to furtherrestrict the class of mechanisms to take into consideration.

11

Lemma 2. There exists an optimal device such that, for everytype profile t ∈ T , the recommended action profile a(t) isunique (i.e., µ is point mass at a(t)) and the restriction of theintervention rule in r = t and m = a(t), i.e., Φa = Φt,a(t),a,sustains without intervention a(t) in Γt.

Proof: See Appendix BLemma 2 suggests the idea to decouple the original problem

into two sub-problems. First, we can calculate the optimalmessage rule µ under the constraint that users adopting therecommended actions have the incentive to report their realtype. Then, it is sufficient to identify an intervention rule Φ ableto sustain µ(t) without intervention in Γt, ∀ t. This is formalizedin the following.

Consider the device D = 〈(Ti), (Ai), µ, X, Φ〉, where

µ = argmaxµ

∑t∈T

π(t)U (µ(t), t, x∗)

subject to:∑t−i∈T−i

π(t | ti)Ui (µ(t), t, x∗) ≥∑

t−i∈T−i

π(t | ti)Ui (µ(t′i, t−i), t, x∗)

∀ i ∈ N, ∀ ti ∈ Ti, ∀ t′i ∈ Ti

and, ∀ t ∈ T , Φa = Φt,µ(t),a sustains without intervention µ(t)in Γt.

Proposition 4. D is an optimal device.

Proof: Lemma 2 guarantees that there exists an optimal de-vice inside the class of devices in which, ∀ t, the recommendedaction profile µ(t) is unique and the restriction of the interven-tion rule in r = t and m = µ(t), i.e., Φa = Φt,µ(t),a, sustainswithout intervention µ(t) in Γt. Among all devices belongingto such class, D is selected to maximize the designer’s expectedutility. Thus, D is an optimal device.

VI. ALGORITHM THAT CONVERGES TO AN INCENTIVECOMPATIBLE DEVICE

In this section we provide a practical tool for the designerto choose an efficient device. Because the optimal device maybe very difficult to compute, even in the decoupled version ofProposition 4, we provide a simple algorithm that converges toan incentive compatible device D in which µ is point mass (i.e.,given a report the recommended action profile is unique) and,although perhaps not optimal, still yields a “good” outcome forthe designer. More precisely, D will sustain without interventionthe honest and obedient strategy profile. The algorithm has beendesigned with the idea to minimize the distance between theoptimal action profile gM (t) and the suggested action profileµ(t), for each possible type profile t. Such an algorithm isrun by the designer to choose an efficient device and can beused when, for every type profile t and at each step of thealgorithm, the designer is able to identify a device for thecomplete information setting that sustains without interventionthe suggested action profile µ(r) in Γr. (Note that the suggestedaction profile will never be lower than the optimal action profilegM (t) or higher than the NE action profile gNE

0

(t) of Γ0t .)

Given a device D in which µ is point mass, we denote byWi(ti, t

′i) the expected utility that user i, with type ti, obtains

reporting type t′i and adopting the suggested action, when theother users are honest and obedient and the intervention devicedoes not intervene, i.e.,

Wi(ti, t′i) =

∑t−i∈T−i

π(t | ti)Ui(µ(t′i, t−i), t, x∗)

Moreover, we say that X and Φr,m,a are induced by µ if thedevice defined by X and Φa(x) = Φr,µ(r),a(x) sustains µ(r)without intervention in Γr, ∀ r ∈ T . If the designer is ableto identify the device defined by X and Γr in the completeinformation setting, then he can easily compute X and Φr,m,ainduced by µ, obtaining a device for the general frameworkthat, by construction, gives the users the incentive to alwaysadopt the recommended actions (i.e., users are obedient) anddoes not intervene (threats of punishments do not need to beexecuted since users follow the recommendations).

The algorithm initializes the device D in the following way:µ(r) = gM (r), X and Φ induced by µ. This means that, giventhe report profile r, the device recommends the optimal (for thedesigner and if user types are r) action profile gM (r) and theusers will adopt it. However, this does not guarantee that theusers are honest: the reported type profile may be different fromthe real one, i.e., r 6= t. To give an incentive for the users to behonest, in each step of the algorithm the recommended actionprofile µ(r) is modified to increase the utility the users obtainif they are honest (or to decrease the utility they obtain whenthey are dishonest). Whenever µ(r) is modified, also X and Φmust be modified accordingly, selecting X and Φ induced byµ such that users remain obedient.

To explain the idea behind the algorithm we exploit Fig.2, where i’s utility is plotted with respect to i’s action, fora fixed type profile t, when all users are honest (i.e., r = t)and the other users are obedient (i.e., gj(tj , µj(t)) = µj(t),∀ j 6= i). Each sub-picture refers to different recommendedactions (i.e., different µ), and in each sub-picture four points aremarked (some of which may possibly coincide) representing thefollowing cases: (1) i adopts the best (for the designer) actiongMi (t); (2) i adopts the recommended action µi(t); (3) i adoptsthe NE action gNE

0

i (t) (notice that it is not the best action foruser i because the other users do not adopt gNE

0

−i (t)); and (4)i adopts the best action hBRi (µ−i(t), t).

The initialization case, in which (1) and (2) coincide, isrepresented by the upper-left Fig. 2. By assumption A6 gMi (t) ≤gNE

0

i (t) and by assumption A5 gNE0

i (t) ≤ hBRi (µ−i(t), t),because µ−i(t) ≤ gNE

0

−i (t). If Wi(ti, ti) ≥Wi(ti, t′i), for every

alternative i’s reported type t′i, then user i has an incentive toreport its true type ti. If, at a certain iteration of the algorithm,this is valid for all users and for all types they may have, thenthe algorithm stops and we obtain a device that sustains without

12

intervention the honest and obedient strategy profile.18

Conversely, suppose there exists a user i and types ti and t′isuch that Wi(ti, ti) < Wi(ti, t

′i), i.e., user i has an incentive

to report t′i when its type is ti. In this case the algorithmincreases the recommended action µi(t) by a quantity equalto εi, moving it in the direction of the best response functionhBRi (µ−i(t), t), for every possible combination of types t−i ofthe other users, and X and Φ must be modified accordingly suchthat users remain obedient. This has the effect, as representedby upper-right Fig. 2, to increase the utility of user i when itis honest, ∀ t−i, which in turn implies that the expected utilityof users i when it is honest (i.e., W (ti, ti)) increases. Thisprocedure is repeated as long as Wi(ti, ti) < Wi(ti, t

′i) and

µi(t) ≤ gNE0

i (t).In case i’s suggested action µi(t) reaches gNE

0

i (t) and stillWi(ti, ti) < Wi(ti, t

′i), then the suggested action of user k,

µk(t), is increased by a quantity equal to εk, ∀ k ∈ N , k 6= i,∀ t−i ∈ T−i. As we can see from lower-left Fig. 2, this meansto change the shape of the curve representing i’s utility withrespect to i’s action. In particular, by assumption A5, the bestresponse function hBRi (µ−i(t), t) is moved in the direction ofthe recommended action µi(t).

If µk(t) reaches gNE0

k (t) as well, ∀ k ∈ N , then µi(t)coincides with the best response function hBRi (µ−i(t), t), asrepresented in the lower-right Fig. 2. In fact, by definition, theNE is the action profile such that every user is playing itsbest action against the actions of the other users. Since µi(t)coincides with hBRi (µ−i(t), t), ∀ t−i ∈ T−i, user i is told toplay its best action for every possible combination of the typesof the other users. Hence, user i cannot increase its utilityreporting type t′i, i.e., it must be Wi(ti, ti) ≥Wi(ti, t

′i).

The algorithm stops the first time every user has an incentiveto declare its real type. Since at each iteration the suggestedaction profiles are increased by a fixed amount, the algorithmconverges after a finite number of iterations. The higher thesteps εi, i ∈ N , the lower the convergence time of the algorithm.On the other hand, the lower the steps, the closer the suggestedaction profile to the optimal one.19

A. Example: a 2–users MAC game

In this subsection we provide a simple example to illustratethe concepts introduced in the last sections and to validate theusefulness of the proposed algorithm.

Consider a MAC problem in which two users, 1 and 2,contend for a common channel. Time is slotted, and in each slotuser i, i = 1, 2, transmits a packet with probability ai ∈ [0, 1],which is chosen by user i at the beginning of the communicationsessions and kept constant. Moreover, in the system there is an

18Notice that, if a maximum efficiency incentive compatible direct mech-anism exists, since it must satisfy the conditions of Proposition 2, then theinitialization of the algorithm corresponds to a maximum efficiency incentivecompatible direct mechanism and the algorithm stops after the first iteration.

19Notice that, since no assumption such as convexity is made for thedesigner’s expected utility, an action profile closer to the optimal one doesnot necessarily imply a better outcome for the designer.

Algorithm 1 General algorithm.1: Initialization: µ(t) = gM (t) ∀ t, X and Φ induced by µ2: For each user i ∈ N and each pair of types ti, t′i ∈ Ti3: If Wi(ti, ti) < Wi(ti, t

′i)

4: If µi(t) < gNE0

i (t) for some t−i ∈ T−i5: µi(t)←min

{µi(t) + εi, g

NE0

i (t)}

, ∀ t−i ∈ T−i6: X and Φ induced by µ7: Else8: µk(t)←min

{µk(t) + εk, g

NE0

k (t)}

, ∀k 6= i, ∀ t−i ∈ T−i9: X and Φ induced by µ

10: Repeat from 2 until 3 is unsatisfied ∀ i, ti, t−i

0

0.5

1

1.5

2

2.5

Ui(a

i, µ

−i(t

), t

, x

* )

ai

0

0.5

1

1.5

2

2.5

ai

Ui(a

i, µ

−i(t

), t

, x

* )

0

0.5

1

1.5

2

2.5

Ui(a

i, µ

−i(t

), t

, x

* )

0

0.5

1

1.5

2

2.5

ai

ai

Ui(a

i, µ

−i(t

), t

, x

* )

gi

M(t) = µ

i(t) g

i

NE0

(t) hi

BR(µ

−i(t), t)

µi(t) = g

i

NE0

(t)gi

M(t)

gi

M(t) µ

i(t) h

i

BR(µ

−i(t), t)

gi

M(t) µ

i(t) = g

i

NE0

(t) = hi

BR(µ

−i(t), t)

gi

NE0

(t)

hi

BR(µ

−i(t), t)

Fig. 2. User i’s utility vs. user i’s action, for different recommended actions

intervention device D that transmits packets with probabilityx ∈ [0, 1]. We assume that a packet is correctly received if andonly if a collision does not occur. Hence, the rate of user i isRi = ai(1 − a−i)(1 − x), where the subscript −i denotes theother user. We consider the following utility functions for theusers and the designer

Ui(a, ti, x) = logRi −aiti

+ ci , i = 1, 2

U(a, t, x) = U1(a, t1, x) + U2(a, t2, x)

where a = (a1, a2), t = (t1, t2), ti ∈ < is the type of user i,and ci is a constant.

The utility of user i is increasing and concave with respectto i’s throughput, and linearly decreasing with respect toi’s transmission probability, that represents i’s average powerconsumption per slot. The type ti, which can be interpretedas the number of transmissions per unit of cost, expresses thetrade–off between the relative importance of throughput andpower for user i.x∗ = 0 represents the “no intervention” action. Ui(a, ti, 0)

is concave with respect to ai, and imposing∂Ui(a, ti, 0)

∂ai= 0,

the resulting NE of the game Γt0 is gNE0

i (t) = ti, i = 1, 2.Also, U(a, t, 0) is jointly concave with respect to a1 and a2,

and imposing∂U(a, t, 0)

∂ai= 0, the resulting optimal action is

gMi (t) = ti +1

2−√t2i +

1

4, i = 1, 2.

It is possible to check that in this case all the conditions

13

A1-A6 are satisfied. Moreover, also the additional assumptionsmade in Section V.B are satisfied. In particular, if the device’spunishments are strong enough (i.e., x is high enough) whensome users do not follow the recommendations, it is possibleto show that every action profile g(t) ≤ gNE

0

i (t) is sustain-able without intervention in Γt (i.e., the complete informationsetting).

Now we consider some numerical examples to describe theresults derived in Sections V and VI. We assume a commonconstant c1 = c2 = 3 (the analysis is independent of theconstant, this choice is made only to obtain positive utilities),a common type set T1 = T2 = {tlow, thigh}, and a user is of aparticular type with probability 0.5, independently of the otheruser’s type. If T1 = T2 = {1/4, 5/6}, it is easy to check thatcondition 2 of Proposition 2 is satisfied, and in fact it is possibleto adopt a maximum efficiency device which asks the usersto report their types (they will be honest to avoid unfavorablerecommendations) and recommends them to adopt the optimalactions (they will be obedient to avoid the punishments).

If T1 = T2 = {1/3, 5/6}, then a maximum efficiencymechanism does not exists. In fact, if the device recommendedthe users to adopt the optimal actions, an honest low type userwould obtain an average utility of 0.84, whereas a dishonestlow type user would obtain an average utility of 0.87, i.e., lowtype users have an incentive to cheat by declaring themselvesto be of high type. To avoid this situation the proposed al-gorithm increases the transmission probabilities recommendedto low type users. If ε = 0.01, after 8 iterations (i.e., therecommended action for a low type user is increased by 0.08)the algorithm converges to an incentive compatible device inwhich the designer utility is 1.63, slightly lower than thebenchmark optimum 1.68, but higher than 0.52, which is theutility obtainable in the absence of an intervention device.

VII. CONCLUSION

In this paper we have extended the intervention frameworkintroduced by [3] to take into account situations of privateinformation, imperfect monitoring and costly communication.We allow the designer to use a device that can communicatewith users and intervene in the system. The goal of thedesigner is to choose the device that allows him to obtain thehighest possible utility in the considered scenario. For a classof environments that includes many engineering scenarios ofinterest (e.g., power control [6], [13], MAC [4], [14], and flowcontrol [14]–[18]) we find conditions under which there existdevices that achieve the benchmark optimum and conditionsunder which such devices do not exist. In case they do not exist,we find conditions such that the problem of finding an optimaldevice can be decoupled. Because the optimal device may stillbe difficult to compute, we also provide a simple algorithm thatconverges to a device that, although perhaps not optimal, stillyields a ‘good’ outcome for the designer. Our work in [19]demonstrates that these non-optimal protocols are very usefulin a flow control management system.

APPENDIX APROOF OF PROPOSITION 2

Proof: We prove ⇒ by contradiction.Let D = 〈(Ti), (Ai), µ,X,Φ〉 be a maximum efficiency

device (remember that we focus only on incentive compatibledevices). Suppose 3 is not valid, i.e., there exists a type profile tsuch that the non-optimal action profile z 6= gM (t) is suggestedwith positive probability µt(z) > 0. Then

EU(f, g,D) =∑t∈T

π(t)∑a∈A

µt(a)∑x∈X

Φt,a,a(x)U(a, t, x)

= V +W + µt(z)∑x∈X

Φt,z,z(x)U(z, t, x)

< V +W + µt(z)U(gM (t), t, x∗) ≤ EU ben (4)

where

V =∑

t∈T,t 6=t

π(t)∑a∈A

µt(a)∑x∈X

Φt,a,a(x)U(a, t, x)

W = π(t)∑

a∈A,a6=z

µt(a)∑x∈X

Φt,a,a(x)U(a, t, x)

The first inequality of Eq. (4) is valid because of A1 and A2,and the last inequality is valid because the benchmark optimumis the maximum achievable. Eq. (4) contradicts the fact that Dis a maximum efficiency device.

Now suppose 4 is not valid, i.e., that Φa = Φt,gM (t),a doesnot sustain without intervention gM (t) in Γt. If Φa does notsustain gM (t) in Γt, then there exists a user i and an actionai 6= gMi (t) such that user i prefers to adopt ai when told touse gMi (t), i.e., the strategy gi(ti, gMi (t)) = ai allows user i toobtain a higher utility with respect to the obedient strategy g∗i ;this contradicts the fact that the device is incentive compatible.If Φa sustains gM (t) in Γt “with intervention”, then the userswill adopt the action profile g∗(t, gM (t)) = gM (t) ∀ t, but thereexists t and x 6= x∗ such that Φt,gM (t),gM (t)(x) > 0. Then

EU(f, g∗, D) =∑t∈T

π(t)∑x∈X

Φt,gM (t),gM (t)(x)U(gM (t), t, x)

= V +W + π(t)Φt,gM (t),gM (t)(x)U(gM (t), t, x)

< V +W + π(t)Φt,gM (t),gM (t)(x)U(gM (t), t, x∗) ≤ EU ben

where

V =∑

t∈T,t 6=t

π(t)∑x∈X

Φt,gM (t),gM (t)(x)U(gM (t), t, x)

W = π(t)∑

x∈X,x 6=x

Φt,gM (t),gM (t)(x)U(gM (t), t, x)

which contradicts the fact that D is a maximum efficiencydevice.

Finally, if 1 is not satisfied then 4 can not be satisfied either(because gM (t) is not sustainable without intervention), thuswe obtain a contradiction. If 2 is not satisfied then either 3 isnot satisfied or the device is not incentive compatible (because,given 3, 2 is a particular case of the incentive-compatibilityconstraints), thus, in both cases, we obtain a contradiction.

14

⇐ Starting from the notion of equilibrium in Eq. (1), it isstraightforward to verify that if 1 − 4 are satisfied the honestand obedient strategy profile (f∗, g∗) is sustained withoutintervention. Hence, the users always adopt the optimal actionprofile gM (t), the device uses the ‘non intervention action’x∗, and the utility of the designer is equal to the benchmarkoptimum defined in Eq. (2).

APPENDIX BPROOF OF LEMMA 2

Proof: Let D = 〈(Ti), (Ai), µ,X,Φ〉 be an optimal device(remember that we focus only on incentive compatible devices).The expected utility of user i having type ti can be written as

EUi(f, g, ti, D) =∑

t−i∈T−i

π(t | ti)Vi(t)

Vi(t) =∑a∈A

µt(a)∑x∈X

Φt,a,a(x)Ui(a, t, x)

Denote by ai(t) the minimum action recommended to useri with positive probability when the type profile is t, i.e.,ai(t) = min {ai ∈ Ai : µt(ai, a−i) > 0, a−i ∈ A−i}. We de-fine the following intervals, ∀ i ∈ {1, . . . , n},

Ii(t) =[amini , min

{ai(t) , g

NE0

i (t)}]

and we use the notation I(t) and I−i(t) in the usual way.We define the function `i(a−i) in the domain I−i(t) as

follows:

`i(a−i) = {ai ∈ Ii(t) such that Ui (a, t, x∗) = Vi(t)}

The function `i is a non-empty set-valued function from I−i(t)to the power set of Ii(t). In fact, ∀ a′−i ∈ I−i(t),

Ui(amini , a′−i, t, x

∗) = 0 ≤ Vi(t) ≤∑a∈A

µt(a)Ui(a, t, x∗)

≤∑a∈A

µt(a)Ui(ai, a′−i, t, x

∗) (5)

The second inequality of Eq. (5) is valid because Ui (a, t, x) ≤Ui (a, t, x∗), ∀ a, t, x. The last inequality of Eq. (5) is validbecause i’s utility is non increasing in the actions of the otherusers and, from the definition of the set I−i(t), a′−i ≤ ai(t) ≤a−i, ∀ a′−i ∈ I−i(t) and ∀ a−i recommended with positiveprobability. Eq. (5) and the continuity of i’s utility imply thatan action ai(t) ∈ Ii(t) satisfying Ui (a, t, x∗) = Vi(t) exists,∀ a−i ∈ I−i(t). Moreover, by definition `i(a−i) has a closedgraph (i.e., the graph of `i(a−i) is a closed subset of I(t)) and,since i’s utility is non decreasing in

[amini gNE

0

i (t)], `i(a−i)

is convex, ∀ a−i ∈ I−i(t).We define the function `(a) = (`1(a−1), · · · , `n(a−n)),∀ a ∈ I(t). The function ` is defined from the non-empty,compact and convex set I(t) to the power set of I(t). Thanksto the properties of `i, ` has a closed graph and `(a) is non-empty and convex. Therefore we can apply Kakutani fixed-pointtheorem [34] to affirm that a fixed point exists, i.e., there exists

an action profile a(t) ∈ I(t) such that Ui (a, t, x∗) = Vi(t),∀ i ∈ N . Notice that a(t) < gNE

0

(t), therefore a(t) issustainable without intervention in Γt, and we denote by Φathe intervention rule that sustains without intervention a(t) inΓt.

Finally, the original optimal device D = 〈(Ti), (Ai), µ,X,Φ〉can be substituted with the device D = 〈(Ti), (Ai), µ, X, Φ〉 inwhich, ∀ t, µ(t) = a(t) and Φt,a(t),a = Φa. With the newdevice D the users are obedient (because the restriction of theintervention rule, Φa, sustains a(t)) and honest (because theutilities they obtain for each combination of reports are thesame as in the initial device D that sustains the honest andobedient strategy profile). More specifically, D sustains withoutintervention the honest and obedient strategy profile. Moreover,in the equilibrium path the users’ expected utilities using Dcoincide with the users’ expected utilities using D; thus, alsothe designer’s utility (which is a function of users’ utilities)remains the same, and this implies that D is optimal.

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Luca Canzian [M’13] received the B.Sc., M.Sc., and Ph.D. degrees inElectrical Engineering from the University of Padova, Italy, in 2005, 2007, and2013, respectively. From 2007 to 2009 he worked in Venice, Italy, as an R&DEngineer at Tecnomare, a company providing design and engineering servicesfor the oil industry. From September 2011 to March 2012 he was on leaveat the University of California, Los Angeles (UCLA). Since January 2013, hehas been a PostDoc at the Electrical Engineering Department at UCLA. Hisresearch interests include resource allocation, game theory, online learning andreal-time stream mining.

Yuanzhang Xiao received the B.E. and M.E. degree in Electrical Engineeringfrom Tsinghua University, Beijing, China, in 2006 and 2009, respectively. He iscurrently pursuing the Ph.D. degree in the Electrical Engineering Department atthe University of California, Los Angeles. His research interests include gametheory, optimization, communication networks, and network economics.

William Zame William Zame (Ph.D., Mathematics, Tulane University 1970)is Distinguished Professor of Economics and Mathematics at UCLA. He previ-ously held appointments at Rice University, SUNY/Buffalo, Tulane Universityand Johns Hopkins University, and visiting appointments at the Institute forAdvanced Study, the University of Washington, the Institute for Mathematicsand its Applications, the Mathematical Sciences Research Institute, the InstitutMittag-Leffler, the University of Copenhagen, VPI, UC Berkeley and EinaudiInstitute for Economics and Finance. He is a Fellow of the Econometric Society(elected 1994) and a former Guggenheim Fellow (2004-2005).

Michele Zorzi [F’07] received the Laurea and the PhD degrees in ElectricalEngineering from the University of Padova, Italy, in 1990 and 1994, respec-tively. During the Academic Year 1992/93, he was on leave at the Universityof California, San Diego (UCSD) as a visiting PhD student, working onmultiple access in mobile radio networks. In 1993, he joined the faculty of theDipartimento di Elettronica e Informazione, Politecnico di Milano, Italy. Afterspending three years with the Center for Wireless Communications at UCSD,in 1998 he joined the School of Engineering of the University of Ferrara, Italy,where he became a Professor in 2000. Since November 2003, he has beenon the faculty at the Information Engineering Department of the University ofPadova. His present research interests include performance evaluation in mobilecommunications systems, random access in mobile radio networks, ad hocand sensor networks, energy constrained communications protocols, broadbandwireless access and underwater acoustic communications and networking.

Dr. Zorzi was the Editor-In-Chief of the IEEE WIRELESS COMMUNICA-TIONS MAGAZINE from 2003 to 2005 and the Editor-In-Chief of the IEEETRANSACTIONS ON COMMUNICATIONS from 2008 to 2011, and currentlyserves on the Editorial Board of the WILEY JOURNAL OF WIRELESSCOMMUNICATIONS AND MOBILE COMPUTING. He was also guest editorfor special issues in the IEEE PERSONAL COMMUNICATIONS MAGAZINE(Energy Management in Personal Communications Systems) IEEE WIRELESSCOMMUNICATIONS MAGAZINE (Cognitive Wireless Networks) and theIEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS (Multi-media Network Radios, and Underwater Wireless Communications Networks).He served as a Member-at-large of the Board of Governors of the IEEECommunications Society from 2009 to 2011.

Mihaela van der Schaar [F’10] is Chancellor’s Professor of ElectricalEngineering at University of California, Los Angeles. Her research interestsinclude network economics and game theory, online learning, multimedianetworking, communication, processing, and systems, real-time stream mining,dynamic multi-user networks and system designs. She is an IEEE Fellow,a Distinguished Lecturer of the Communications Society for 2011-2012, theEditor in Chief of IEEE Transactions on Multimedia and a member of theEditorial Board of the IEEE Journal on Selected Topics in Signal Processing.She received an NSF CAREER Award (2004), the Best Paper Award from IEEETransactions on Circuits and Systems for Video Technology (2005), the OkawaFoundation Award (2006), the IBM Faculty Award (2005, 2007, 2008), the MostCited Paper Award from EURASIP: Image Communications Journal (2006), theGamenets Conference Best Paper Award (2011) and the 2011 IEEE Circuits andSystems Society Darlington Award Best Paper Award. She received three ISOawards for her contributions to the MPEG video compression and streaminginternational standardization activities, and holds 33 granted US patents. Formore information about her research visit: http://medianetlab.ee.ucla.edu/