Regional concentration of entrepreneurial activities

This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution

and sharing with colleagues.

Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third party

websites are prohibited.

In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further information

regarding Elsevier’s archiving and manuscript policies areencouraged to visit:

http://www.elsevier.com/authorsrights

http://www.elsevier.com/authorsrights

Author's personal copy

Journal of Economic Behavior & Organization 102 (2014) 59–73

Contents lists available at ScienceDirect

Journal of Economic Behavior & Organization

j ourna l h om epa ge: w ww.elsev ier .com/ locate / jebo

Regional concentration of entrepreneurial activities

Graciela Kuechle ∗

Batten Institute, Darden School of Business, University of Virginia, 100 Darden Blvd, Charlottesville, VA 22906, United States

a r t i c l e i n f o

Article history:Received 13 March 2012Received in revised form 12 March 2014Accepted 17 March 2014Available online 25 March 2014

JEL classification:L26R12C73F16

Keywords:EntrepreneurshipRegional concentrationEvolutionary game theoryMarket entry gamesSpatial mobility

a b s t r a c t

Entrepreneurial agglomerations often feature positive feedback mechanisms such as strate-gic complementarities, knowledge spillovers and network externalities. However, theycan also occur in the absence of these mechanisms, even across regions of considerablyhomogeneous economic potential. We analyze a market entry game in an evolutionarysetup to investigate how two economically similar regions may evolve different rates ofentrepreneurship under the assumption that there is migration between them, and thatindividuals are predisposed to imitate others who are economically more successful. Weexamine the long run dynamics of this model and assess the impact of the economic, socialand demographic exchange on the regional concentration of entrepreneurial activities.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

It is a well-established fact that entrepreneurial undertakings are susceptible to geographic concentration (Acs andVarga, 2005; Cooper and Folta, 2000; Glaeser et al., 2010a). Data on new firm formation and self-employment show thatentrepreneurial activity varies considerably across regions, states and cities (Acs and Malecki, 2003; Armington and Acs,2002; Reynolds et al., 1995), and that this phenomenon persists over time (Acs and Mueller, 2008; Andersson and Koster,2010; Fritsch and Mueller, 2007).

Theories of industry agglomeration are commonly used to explain regional differences in entrepreneurship (Cooper andFolta, 2000; Glaeser et al., 2010b). According to this literature, the basic sources of agglomeration economies are backwardand forward linkages accruing from labor market pooling and input sharing (Marshall, 1920), knowledge spillovers stemmingfrom information transfer between individuals in different organizations (Acs et al., 1992; Audretsch and Lehmann, 2005) andnetwork externalities arising from the collective adoption of behaviors (Aldrich and Zimmer, 1986; Minniti, 2005). SiliconValley and Boston’s Route 128 are archetypical cases of a cluster of entrepreneurship that developed in the simultaneouspresence of these three types of externalities, with support coming from novel technologies, prestigious universities, andeffective social networks (Audretsch and Feldman, 1996; Orsenigo, 2006; Saxenian, 1994). Nevertheless, low-tech sectors

∗ Tel.: +49 211 6910011.E-mail address: [email protected]

http://dx.doi.org/10.1016/j.jebo.2014.03.0170167-2681/© 2014 Elsevier B.V. All rights reserved.


60 G. Kuechle / Journal of Economic Behavior & Organization 102 (2014) 59–73

also host entrepreneurial agglomerations, and similarly endowed regions evolve idiosyncratic levels of entrepreneurialactivity (Ellison and Glaeser, 1997; Ellison et al., 2010; Krugman, 1991b; Strange, 2009).

Research on entrepreneurial agglomerations focuses on the positive externalities derived from the interaction betweenincumbent and potential entrepreneurs (Cooper and Folta, 2000). Newcomers to a region, spin-offs and late adopters of atechnology, all benefit from the availability of specialized inputs and the reduction of environmental uncertainty resultingfrom the efforts of those who pioneered early developments (Acs and Varga, 2005; Arthur, 1994; Klepper, 2007, 2010;Minniti, 2005). Yet this paper argues that, besides the mutual reinforcement of entrepreneurial actions there is anothermechanism that could produce an uneven distribution of entrepreneurial activities across regions, namely the strategicinteraction between individuals who face the decision of whether to enter a certain market.

In the extant frameworks of entrepreneurial agglomerations (Minniti, 2005; Strange, 2009), disparities across regionsresult from the existence of multiple equilibria so that regions with diverse initial conditions and idiosyncratic historicalpaths lock into different rates of entrepreneurship (Arthur, 1989; Matsuyama, 2002). In these models, the geographical areasdo not interact with each other; they follow independent fates. Yet, despite the fact that culture, social ties and financialconstraints hinder spatial mobility, migration remains a pervasive demographical regularity. For instance, during the lastsixty years, 5.23% of the U.S. population migrated on average every year to another county, state, division or region with aremarkably low standard deviation of 0.12 (U.S. Census Bureau, 2008). Therefore, it becomes indispensable to explore therole played by demographic mobility on the persistence of spatial concentrations of entrepreneurial undertakings.

Interactions between regions are not confined to population and economic exchange. They also extend to the culturalarena. Entrepreneurs, for instance, resort to cues, information and knowledge available in their social environment in orderto mitigate uncertainty and facilitate decision-making (Aldrich, 1979; Granovetter, 1985; Kim and Aldrich, 2005). Further-more, individuals have a propensity to imitate the behavior of prestigious and successful people, especially in situationscharacterized by complexity and little understood relationships (Richerson and Boyd, 2005). These forms of cultural learn-ing affect preferences, beliefs, attitudes towards novelty, and even career choices. Admittedly, the diffusion of informationand the observation of behaviors decay with spatial and relational distance (Audretsch and Feldman, 1996; Anselin et al.,1997; Jaffe et al., 1993). Yet these forms of cultural transmission have the potential to unleash path-dependent processesthat lead, over time, to the entrenchment of start-up activity and the emergence of an entrepreneurial culture (Fritsch andWyrwich, 2012; Minniti, 2005; Saxenian, 1994).

These facts raise the question on the types of conditions that could lead spatially separated but economically and culturallyinterconnected regions to evolve different levels of entrepreneurial activity, if they have similar economic potential, there ismigration, and individuals are predisposed to imitate others who are economically more successful. Following Henrich andBoyd (2008) we develop a cultural evolutionary game theoretic model of regional concentration in which individuals decidebetween entrepreneurship and paid employment. At the beginning of every period, individuals are matched pairwise toplay a market entry game. After playing the game, they compare their just earned payoffs with those of another individualchosen at random. Based upon this comparison, they assess whether to continue with their previous occupation or toswitch. Ultimately, a percentage of the population in each region migrates to the other. We study the evolution and long-runproperties of this dynamic system to assess the parametric conditions that foster the emergence and persistence of regionswith idiosyncratic levels of entrepreneurial activity.

2. Theoretical and empirical underpinnings of entrepreneurial agglomerations

What forces lead entrepreneurs to co-locate? A basic rationale, which probably accounts for the earliest concentrations,relies on the existence of natural advantages, understood as immobile inputs that are essential for production (Ellison andGlaeser, 1997, 1999; Fujita et al., 1999). For instance, natural advantages explain the setting up of the wine industry inCalifornia, early industrial sites near coalfields and the location of old cities near water bodies (Ellison and Glaeser, 1999).This type of geographical externality explains not only why entrepreneurs agglomerate but also why they choose particularsites, providing a proper theory of location. However, empirical evidence indicates that most patterns of concentrationscannot be fully accounted for by such intrinsic and permanent differences among locations (Ellison and Glaeser, 1999).

An alternative rationale is that entrepreneurs co-locate because of externalities arising from their mutual interaction.Along these lines, existent explanations for entrepreneurial agglomerations follow Marshall (1920) in hypothesizing thatentry into a concentrated industry allows firms to reap the benefits of a pooled market for skilled workers, supports thesharing and production of specialized inputs and fosters informational spillovers among firms in relation to productiontechniques, suppliers and customers. These ideas have triggered three streams of research on entrepreneurial concentrationsbased respectively on backward and forward linkages, knowledge spillovers and network externalities. In this section webriefly discuss the contributions, both theoretical and empirical, related to our model.

2.1. Entrepreneurship in the New Economic Geography

The New Economic Geography provides a general framework to understand how a virtuous circle of entrepreneurialactivity can emerge from the interplay between increasing returns and pecuniary externalities originating from demandand supply linkages (Fujita et al., 1999; Krugman, 1991a). Increasing returns to scale encourage production to becomeconcentrated in a limited number of sites, whereas expensive transportation costs induce firms to locate in the proximity


G. Kuechle / Journal of Economic Behavior & Organization 102 (2014) 59–73 61

of the customers, raw materials and labor force. As co-location gives ipso facto rise to large markets through backward andforward linkages, the attempt to concentrate in areas where markets are large becomes a self-fulfilling prophecy (Arthur,1994; Fujita et al., 1999; Krugman, 1991a).

The basis of the New Economic Geography paradigm is the core-periphery model. In its continuous time version, themodel has two possible long-term behaviors, namely, concentration or diversification of economic activity. Starting from asymmetric equilibrium, a fall in transportation costs beyond certain levels leads to catastrophic agglomeration and whichevercountry or region happens to be the first to host the manufacturing concentration will hold on to this advantage indefinitely(Neary, 2001). The dynamics become more complex in the discrete-time version of the model, which, in addition to cata-strophic agglomeration and hysteresis, may exhibit the periodic or chaotic coexistence of two active manufacturing sectors(Currie and Kubin, 2006).

The underlying model of New Economic Geography illustrates regional divergence in terms of the relative strength oftransportation costs, economies of scale and labor intensity. Since it assumes free entry (or more precisely, a perfectly elasticsupply of firms), it offers no room for strategic interaction or entrepreneurial decision-making (Neary, 2001; Glaeser et al.,2010b).

Forslid and Ottaviano (2003) depart from this tradition with a core-periphery model in which high-skilled entrepreneurshire low-skilled workers to produce varieties of manufactured goods.1 High-skilled individuals are free to move betweenregions but are bound to become entrepreneurs. Low-skilled individuals, on the other hand, are spatially constrained but canswitch between working in agriculture and manufacturing. Although this model deals with entrepreneurship, it falls shortof providing a proper setup for entrepreneurial decision-making. The reason is that skilled workers are bound to choose aparticular occupation, which leads to a completely inelastic global supply of entrepreneurs. In contrast, our model allows thesupply of entrepreneurship to fluctuate with expected payoffs, while assuming equally skilled individuals, cultural learningand mobile workers.

Glaeser et al. (2010b) avoid the limitations of the footloose entrepreneur model of Forslid and Ottaviano by assuming thatindividuals choose between entrepreneurship and paid employment. In their model, utility maximizing entrepreneurs makea production decision before knowing whether their products will be traded in the other region. Although the entrepreneursare not mobile, the workers are free to migrate between regions in response to wages. The main result is that entrepreneurshipincreases with demand and thus with city population and decreases with fixed costs. Because of the virtuous circle thatmarket size induces, the model predicts that larger areas will have higher levels of entrepreneurship. Our model complementsGlaeser et al. (2010b) by assuming strategic interactions in the form of a market entry game with cultural learning and mobileentrepreneurs.

2.2. A matching model of entrepreneurial decision-making

Strange (2009) offers an alternative microfoundation to the New Economic Geography by explaining regional diversitywith a model of strategic interaction in which entrepreneurs are matched with workers. In the first stage, the individualschoose between the two roles. In the second stage, the entrepreneurs are matched with their nearest workers. The valueof the match decreases with the relative distance between the entrepreneur and the workers and the congestion caused byagglomeration. If the entrepreneurs and workers have a coincident location, the match is perfect; otherwise, the entrepreneurincurs adjustment costs. Entrepreneurs are evenly distributed around the unit circle, whereas the workers’ addresses arerandom draws from a uniform distribution and unknown to them ex-ante. Workers earn a wage that depends on the distanceto the entrepreneur that hired them, and entrepreneurs earn the residual from all their matches.

The goal of this model is to describe a process by which large cities foster the emergence of thick markets that furtherexpand the possibilities for matching. The basic logic is that an increase in the population raises the number of possi-ble matches, thereby encouraging entrepreneurship. This in turn generates agglomerations that are bound by congestioncosts. The model’s main prediction is that thicker markets lead to higher wages (due to higher productivity) and moreentrepreneurial activity (via a richer range of complementary activities).

In this model the individuals are heterogeneous in terms of location, which affects the values of their matches. Fur-thermore, there is no migration. Our model complements Stranger’s framework by dealing with a market-entry game,homogenous individuals, migration and cultural learning.

2.3. Entrepreneurship and network externalities

Social network externalities are non-pecuniary gains accruing to individuals in a social network in the form of ambiguityreduction, legitimization of activities, vicarious learning, and access to specialized information (Aldrich and Zimmer, 1986;Cooper and Folta, 2000; Minniti, 2005; Saxenian, 1994; Thornton and Flynn, 2003). Network externalities are of utmostimportance to technological start-ups as they usually lack human and financial resources (Acs and Audretsch, 2005; Cooperand Folta, 2000; Feldman, 1993; Minniti, 2005).

1 Commendatore et al. (2008) and Commendatore and Kubin (2013) extend this analysis to discrete time and three regions, respectively.



From a static or short-run perspective, models of network externalities argue that entrepreneurs co-locate becausetheir social networks are already localized (Stuart and Sorenson, 2003). From a dynamic or long run point of view, thesemodels portray agglomerations as the outcome of coevolutionary processes characterized by strategic complementaritiesand sequential decision-making (Arthur, 1989; Dosi, 1997; Minniti, 2005).

Minniti (2005) develops a dynamic model of network externalities in which individuals sequentially decide betweenentrepreneurship and paid employment based on the observation of prior behaviors and outcomes. In this model, the indi-viduals are heterogeneous with respect to their employment opportunities and preferences between work and leisure. Theyaim to maximize their returns and have idiosyncratic thresholds that specify the size of the community of entrepreneurs,or the amount of ambiguity reduction, that triggers their decision to join the group. Individual actions are strategic comple-ments: they mutually reinforce one another. The main result of this model is that the final level of entrepreneurial activitydepends upon the sequence of choices and the distribution of thresholds. In this manner, the prior history may direct regionsto develop different rates of entrepreneurship.

In contrast to the models in the tradition of the New Economic Geography, this model portrays no interaction betweenthe regions and no migration to anchor the dynamics into different paths. Our model complements Minniti’s by consideringa market entry game in which actions are strategic substitutes instead of complements, a game theoretic set-up in whichtwo regions interact with each other featuring homogenous individuals and migration.

2.4. Empirical evidence on entrepreneurial agglomerations

Although we have a rich theoretical knowledge regarding the nature of clusters and agglomerations, a complete accountof the specific sources of entrepreneurial agglomerations remains elusive (Thornton and Flynn, 2003; Glaeser et al., 2010b).There is evidence for the existence of agglomeration forces such as input–output linkages (Armington and Acs, 2002; Ellisonet al., 2010), knowledge spillovers (Armington and Acs, 2002; Audretsch and Feldman, 1996; Audretsch and Lehmann, 2005)and network externalities (Aldrich and Zimmer, 1986; Saxenian, 1994); however, the absolute and relative strengths of theseforces remain unassessed (Duranton and Puga, 2004; Strange, 2009).

Entrepreneurial agglomerations have been found to depend on some determinants of start-up activity such as education,skill level of the workers, supply of entrepreneurs, fixed costs, market size, income, wealth, venture capital industry andpopulation growth (Andersson and Koster, 2010; Armington and Acs, 2002; Doms et al., 2010; Fritsch and Mueller, 2007;Fritsch and Wyrwich, 2012; Glaeser et al., 2010a; Reynolds et al., 1995). However, some studies have found no trace of lowercosts of production, high density of customers and suppliers, R&D resources or higher entrepreneurial returns behind thevariation in the founding of new firms (Glaeser et al., 2010a; Reynolds et al., 1995).

Most studies that focus on natural advantages or variables that correlate with entrepreneurial concentrations remaincautious about causality not only because of measurement problems but also because of endogeneity concerns (Glaeseret al., 2010a). For instance, several frameworks predict that wages and productivity as well as entrepreneurial activity willbe higher in thicker markets as well as entrepreneurial activity (Strange, 2009). Indeed, larger cities tend to have a more skilledworkforce despite also hosting larger proportions of high- and low-skilled workers (Andersson and Koster, 2010; Doms et al.,2010; Strange, 2009). However, to the extent that human and capital resources are mobile, the co-location of skilled workersand entrepreneurs as well as other attributes of entrepreneurial concentrations are more likely to be a consequence thana cause of agglomerations (Matsuyama, 2002). Agglomerations are likely to be a manifestation of coevolutionary processesrather than a necessary outcome of a certain set of initial conditions as in unidirectional causal phenomena (Gordon andMcCann, 2000; Orsenigo, 2006). In fact, studies show that a large part of the variation in the regional start-up rates canbe explained by previous start-up activity. This supports the hypothesis that path-dependent processes contribute to theemergence of a propitious environment for entrepreneurship (Andersson and Koster, 2010; Glaeser et al., 2010a; Fritsch andWyrwich, 2012).

The empirical studies mentioned above fall into two basic categories. The first category portrays spatial agglomerations asa manifestation of intrinsic and unique forces. The second one conceives of them as the expression of chance acting upon moreor less qualitatively similar systems. To understand how they relate, consider the case of economic and social institutions.It has been argued that certain countries, regions and clusters are more developed or resilient than others because of theirinstitutions, culture and industrial systems (Acemoglu, 2009; Saxenian, 1994). If we accept that entrepreneurial undertakingsare embedded in social systems (Granovetter, 1985) that are themselves the result of evolutionary processes (Richerson andBoyd, 2005), then we should entertain the possibility that any intrinsic superiority may itself stem from chance acting uponoriginally homogeneous populations. In this respect, we argue that models like ours, which explain how diversity evolvesfrom an initial similarity, depict a more general mechanism that may have been at work in most agglomerations (Leppäläand Desrochers, 2010; Henrich and Boyd, 2008).

All of the models reviewed in this section avoid relying on exogenous drivers of regional diversity and as a consequencenecessitate multiple equilibria. But these models differ in the choices they allow for individuals and in how they han-dle interregional exchange, mobility and individual characteristics. To our knowledge there is no formal dynamic modelof regional variation of entrepreneurial activities simultaneously dealing with (i) a population of individuals who choosebetween actions that are strategic substitutes, (ii) homogeneous individuals in terms of their skills, (iii) migration of bothentrepreneurs and non-entrepreneurs, (iv) myopic decision making, (v) interaction between regions and (vi) imitation of



successful behaviors. These assumptions are empirically valid and since they offset regional differences, they pose a challengeto the emergence of agglomerations.

3. A model of entrepreneurial concentration

It is difficult to capture the entrepreneurial phenomenon within one game, not only because of its complexity but alsobecause of its diversity. Individuals may become entrepreneurs by creating a new firm, by buying an existing one, by goinginto self-employment, or by introducing a new product or creating a new market (Parker, 2009). All of these forms entaileither some kind of risk or a new market entry. These are the two aspects we aim to focus upon in this paper.

Drawing from recent contributions in anthropology and entrepreneurship (Henrich and Boyd, 2008; Kuechle, 2009), webuilt a simple evolutionary game theoretic model. The model consists of a large population of homogenous individuals whoare randomly paired to play a market entry game. Market entry games can be considered the first stage in a two-stageoligopoly game in which players decide first whether to enter or to introduce an innovation and then how much to supply.If all the subgames in the second stage have uniquely defined equilibria, the market entry game can be interpreted as atruncation of the original two-stage game (Selten and Güth, 1982).

Consistent with our research question, we consider a population of homogeneous individuals who may enter a market tobecome entrepreneurs (E) or stay out to become employees (∼E). The payoff matrix is displayed in Table 1. If only one playerenters, the payoffs are � to the entrant and w to the player who stays out. If both players enter the market, competition –represented by the existence of a market capacity – drives the individual profits down by an amount equal to C. No entrance(∼E) yields a safe payoff equal to w. As usually assumed in these types of games, market entry entails a worse payoff than asafe job when both players enter and a higher payoff when only one enters the market (i.e., w < � < w + C).

Market entry games focus on entry coordination and abstract from the economic processes underlying individual payoffs.Variables such as profit and wage are exogenously given and, in the case of symmetric market entry games, are identicalfor all players. This modeling option is justified in our case for three reasons. First, we are only concerned with one sectoror market instead of two as in the New Economic Geography. In that literature, the differences in technology, tastes andtransportation costs between agriculture and manufacturing determine not only production and consumption, but locationas well. Therefore, they cannot be left outside the model. In our framework, fundamental factors such as tastes and technologyare supposed to determine the demand and supply, which in turn regulate profit, wage and entry. We exclude them fromthe model because they do not affect the logic of entry into a single market. Second, our analysis focuses on the strategicelements of entry. If we assumed endogenous profits and wages as well as free entry, as in the New Economic Geographyliterature, we would eliminate the strategic aspects we aim to capture. Finally, because our research question is concernedwith homogeneous individuals and regions, it does not necessitate further microfoundations beyond � and w.

In a market entry game, individuals are better off if they can choose non-coincident strategies because those individualswho enter the market will meet others who stay out and obtain higher payoffs on average. Admittedly, pairwise interactionsof this type assume an extremely small market capacity. But this assumption is not restrictive, as the results obtained forpairwise interactions can be extended without loss of generality to situations in which the capacity of the market is higherthan one (Kuechle, 2009). We adopt this assumption because it simplifies the exposition while perfectly capturing the entryphenomenon.

In evolutionary game theoretic set-ups, individuals do not attempt to anticipate the choices of the others, and they followsimple heuristics that are responsive to the payoffs received by each strategy in the population, as in reinforcement learningalgorithms and other types of boundedly rational decision rules (Hofbauer and Sigmund, 1998). This is a valid assumptionwhen modeling entrepreneurs, who usually operate in novel scenarios and therefore lack relevant data to enable rationalbeliefs and forward looking behavior (Minniti, 2005; Parker, 2009). According to the payoff matrix in Table 1, the expectedpayoff to entrepreneurship is given by IE = (� − pC), where p is the probability of being paired with another entrepreneur,and the expected payoff to paid employment is given by I∼E = w.

The population in this model is located in two separate regions, which we refer to as regions 1 and 2. The proportion ofindividuals choosing E in region 1 is labeled p1 and the proportion of individuals choosing E in region 2 is termed p2 (0 < pi < 1;i = 1, 2). As we always compare payoffs at the same point in time, we omit the subscripts denoting the time periods. At thebeginning of every period, each individual interacts with another one, selected at random. We start with the general casethat allows for interaction (or economic exchange) between regions. We follow Henrich and Boyd (2008) by assuming thatthere is a probability d that an individual is paired with a randomly selected individual from the other region, so that the

Table 1Pairwise interaction of the symmetric market entry game.

E ∼E

E � − C, � − C �, w∼E w, � w, w



Table 2Social learning within regions for individuals in region i (i = 1, 2).

Sst Sm

t Pr(Sst , Sm

t ) Pr(Et+1/Sst , Sm

t ) Pr(∼Et+1/Sst , Sm

t )

Et Et P2i

1 0Et ∼Et Pi(1 − pi) 0.5[1 + b(IE

i− I∼E

i)] 0.5[1 + b(I∼E

i− IE

i)]

∼Et Et Pi(1 − pi) 0.5[1 + b(IEi

− I∼Ei

)] 0.5[1 + b(I∼Ei

− IEi)]

∼Et ∼Et (1 − pi)2 0 1

probability that an individual interacts with a co-located person is 1 − d. The expected payoffs to entrepreneurship and paidemployment in regions 1 and 2 is given by

IE1 = d(� − p2C) + (1 − d)(� − p1C) (1)

IE2 = d(� − p1C) + (1 − d)(� − p2C)

I∼E1 = I∼E

2 = w.

when d = 0 the individuals interact only with people located within their own region and when d = 1 they only interact withindividuals in the other region. In this last case, if an individual in region 1 chooses E and interacts with an individual inregion 2, her expected payoff is given by IE

1 = � − p2C. Similarly for an individual in region 2 who interacts with another inregion 1 the expected payoff is given by IE

2 = � − p1C. Note that even if d = 0 is a priori an apparently natural assumption, weshould expect economic exchange and other forms of interactions between the regions to drive the value of d further awayfrom 0. For instance, d could be assumed to be the probability that two agents from different regions enter into a competitionto introduce a new product. Notice that the effect of d on the expected payoff to entry IE

idepends on the relative values

of pi and pj. If pi > pj an increase in d increases the expected revenues of the potential entrepreneurs in region i because itincreases the likelihood of an interaction with an individual in region j which has a lower rate of entrepreneurship thanregion i. Under these circumstances, potential entrepreneurs face lesser chances of reducing their payoffs by C – the cost ofover entry – the higher the value of d. If on the other hand pi < pj, an increase in d decreases the expected revenues of thepotential entrepreneurs in region i because it increases the likelihood of interaction with an individual in region j which hasa higher rate of entrepreneurship than region i. In this scenario the higher values of d increase the chances of over entry.

3.1. Social learning

Consistent with models of cultural evolution, in which successful behaviors are disseminated through observationallearning, imitation and teaching (Richerson and Boyd, 2005), we assume that, after having interacted, individuals havea chance to compare their just earned payoffs with those of another individual. In this way the model accounts for theinfluence of social learning in occupational choice. If two matched individuals receive the same earnings, they stick to theirstrategy. Otherwise, the player with the lower payoff increases the probability of switching to the more successful strategyin proportion to the parameter b (0 < b < 1), which represents the impact of success-biased learning on individual preferences(Henrich and Boyd, 2008).

Based on McElreath and Boyd (2007) and Henrich and Boyd (2008), Table 2 characterizes all possible scenarios of sociallearning for an individual in region i (i = 1, 2) who compares her payoffs with a randomly chose individual in the same region.The first two columns show the four possible combinations of strategies played at time t by an individual who engages insocial learning (the self) and another with whom she compares her payoffs (the model). These strategies are labeled (Ss

t ) and(Sm

t ) respectively. Column three shows the probabilities of occurrence of these four combinations and the last two columnsdepict the chances that the individual who engages in social learning chooses E and ∼E next period.

Notice that the comparison of payoffs by two individuals who chose the same strategy (be it E or ∼E) induces no switch(i.e., Pr(E/E, E) = 1 and Pr (∼E/∼E, ∼E) = 1). The reason is obvious, as there is no alternative. However, it is interesting to notethat individuals do not need to have earned the same payoff even when they choose the same strategy, provided payoffsare frequency dependent. For instance, if two individuals who chose E meet, the possible payoff combinations are [(� − C),(� − C)], [�, (� − C)], [(� − C), �] and [�, �], and their realization depends upon the frequency of the individuals choosing Eand ∼E in the corresponding region during the previous period.

As revealed by the formulae in the last two columns of Table 2, only when individuals choose different strategies canthere be switching effects. If the strategies compared earned the same payoff during the corresponding period, there is a0.5 probability of choosing any of the two strategies (baseline probability) and the decision is said to be unbiased. If on theother hand, the strategies compared earned different payoffs, success-biased learning occurs. The strength of this learningeffect is proportional to the difference in payoffs and the extent to which the behavior of the other individuals affects one’sown preferences, captured by the parameter b. The higher the value of b, the more the individuals are likely to switch to thestrategy with the higher payoff. For instance, if IE

1 − I∼E1 > 0, the chances of choosing E in the next period are higher than

0.5, whereas if I∼E1 − IE

1 > 0, the chances of choosing ∼E in the next period are higher than 0.5. When b = 0, the individuals



are equally likely to choose E and ∼E next period. Since the probabilities in the last two columns need to lie in the interval[0, 1], the parameter b is constrained to lie in the intervals [−(� − piC − w)−1, (� − piC − w)−1] (i, j = 1, 2; i /= j).

3.2. Migration

Success-biased learning is not the only mechanism underlying the change in the rate of entrepreneurial activity. The othersource is spatial mobility. Entrepreneurs are constrained in their choice of start-up location, yet evidence shows that someindustries exhibit entrepreneurial and organizational mobility (Cooper and Folta, 2000; Kerr, 2010). Furthermore, data onthe domestic migration in the US shows a clear and persistent pattern of moderate but general mobility (U.S. Census Bureau,2008). To account for such a phenomenon we assume that at the end of each round, after having compared strategies, aproportion m of the population migrates to the other region.

According to this pattern of spatial mobility, at the end of each period the frequency of entrepreneurs in region i decreasesby pi m and increases by pj m. The fact that m is exogenously given means that migration motivated by the expectation of ahigher expected income (success-biased migration) could not occur. We make this assumption as a first step for two reasons.First, it enables analytical results and second, it captures the plethora of factors exogenous to this model that have been foundto affect migration, such as the proximity to family and friends, social embeddedness, living conditions, etc. For instance,whereas technical and scientific workers have been found to migrate to locations in which innovative activities flourish(Kerr, 2010) they have also been found to trade off substantial income potential in order to remain close to their friends andfamily (Dahl and Sorenson, 2010). In the Appendix we relax this assumption and reassess the dynamics of the model. As itturns out, success-biased migration increases the likelihood of stable agglomerations. This means that the assumption ofexogenous m is rather conservative in terms of identifying the conditions for the existence of entrepreneurial concentrations.

3.3. The dynamics of the model

The crux of evolutionary game dynamics is to determine how a given behavior is likely to evolve given the initial conditionsand a mechanism of replication. Let pi (i = 1, 2) denote the proportion of entrepreneurs in the population of region i at thebeginning of period t. Our task consists in deriving an equation for pi at t + 1 as a function of pi at t and the parametersof the model in order to construct a difference equation for the dynamics of pi. In the present model, the proportion ofentrepreneurs in each region changes because of social learning and migration.

In models of social learning, strategies disseminate when more individuals are willing to adopt them (Richerson and Boyd,2005). People adopt a strategy either because they have experienced its success or because they have observed others whowere successful after adoption. As explained in Section 3.1, in our model, individuals adopt a strategy and then revise theirinformation by observing the performance of a randomly chosen behavior. Given pi at time t, the proportion of entrepreneursin the next period after this form of social learning is given by

Li(pi) = Pr(E/E, E)Pr(E, E) + Pr(E/E, ∼E)Pr(E, ∼E) + Pr(E/∼E, E)Pr(∼E, E) + Pr(E/∼E, ∼E)Pr(∼E, ∼E)

Plugging the values from Table 2, we can rewrite this equation as

Li(pi) = p2i + pi(1 − pi)0.5[1 + b (IE

i − I∼Ei )] + (1 − pi)pi 0.5[1 + b (IE

i − I∼Ei )] (i, j = 1, 2; i /= j)

The one-step change in the proportion of entrepreneurs in region i after social learning is then given by

�pLi = Li(pi) − pi = pi(1 − pi) b(IE

i − I∼Ei ) (2)

According to this basic replicator dynamics equation, the direction and magnitude of change in the behavior E depends onthe variance in behaviors in the population [pi(1 − pi)] and the relative payoffs to the different behaviors (IE

i− I∼E

i).

Now we can add the effect of migration to Eq. (2). After migration, the proportion of individuals who choose E is Mi(pi, pj) = pi + m (pj − pi) so that the change in pi due to migration equals

�pMi = Mi(pi, pj) − pi = m(pj − pi) (3)

In general the dynamics of a behavior change depend upon the order of learning and migration so that Mi[Li(pi),pj] /= Li[M(pi, pj)]. But if the change in the one-time step of the frequency of behaviors is small enough, we can ignorethe lower order effects and define the frequency of entrepreneurs in the next period as the summation of both effects,�pi = �pL

i+ �pM

i, which yields the following system of difference equations for the one-time step change in p1 and p2

�p1 = p1(1 − p1)b(IE1 − I∼E

1 ) + m(p2 − p1)

�p2 = p2(1 − p2)b(IE2 − I∼E

2 ) + m(p1 − p2),(4)

where IEi

and I∼Ei

(i = 1, 2) represent the expected payoffs accruing to the individuals located in regions 1 and 2 from thechoice of entrepreneurship and paid-employment, respectively. The first term of this difference equation represents theeffect of success-biased social learning, whereas the second term represents the change in the proportion of entrepreneursdue to migration.



Using Eq. (1), we can express the expected payoffs to E and ∼E in region 1 as IE1 = d(� − p2C) + (1 − d)(� − p1C) and

I∼E1 = w. The final expression for (4), namely the one-step change in the frequency of entrepreneurs in regions 1 and 2, as a

function of the parameters and current frequencies of entrepreneurs in both populations is given by

�p1 = p1(1 − p1)b[d(� − p2C) + (1 − d)(� − p1C) − w] + m(p2 − p1)

�p2 = p2(1 − p2)b[d(� − p1C) + (1 − d)(� − p2C) − w] + m(p1 − p2).(5)

3.4. Equilibria

The equations for �p1 and �p2 describe the evolution in one-time step of the frequencies of entrepreneurs in regions1 and 2 as a function of individual behaviors, cultural learning and migration. To analyze the dynamics of this system ofinterdependent regions we first identify stable equilibria. Equilibria are combinations of frequencies of entrepreneurialactivity such that no further change occurs once they are reached. An equilibrium is considered locally stable if the systemreturns to it after the occurrence of small perturbations.

The autarkic version of this game, which consists of the model with only one region, has a unique evolutionary stableequilibrium where the proportion of entrepreneurs is given by p* = [(� − w)/C] (Kuechle, 2009). When the frequency ofentrepreneurs reaches this level, no individual has incentives to switch occupations. The fact that this equilibrium is globallystable indicates that regardless of the initial conditions and the size of the perturbations, the system will return to it. Thetwo-region model that we consider in this paper has a different structure due to the interactions among the regions builtinto the processes of migration and social learning.

To study the dynamics of the system (5), we set �p1 = �p2 = 0, d = 1 and look for the solutions, p∗1 and p∗

2, to the system oftwo equations in two unknowns. We express p∗

1 and p∗2 to denote the equilibrium frequencies of entrepreneurs generically.

The system of equations (5) is quadratic in p1 and p2, and therefore, has several equilibria. Apart from two trivial equilibria,namely, p∗

1 = p∗2 = 0 and p∗

1 = p∗2 = 1, which are never stable, our dynamic system has one non-agglomeration equilibrium

where (pNA1 = pNA

2 = pNA = [(� − w)/C]) and two agglomeration-equilibria in which each region displays a different level ofentrepreneurship. Note that the rest point pNA = [(� − w)/C] coincides with the autarkic solution. In such an equilibrium,the probability of adoption of entrepreneurship increases with the expected profit in the absence of competition (�) anddecreases with the opportunity cost of entry (w) and the expected individual losses due to competition (C). Such an equi-librium can be achieved either by a population consisting of a proportion pNA of entrepreneurs and a proportion 1 − pNA ofemployees or by a population in which every individual adopts entrepreneurship with a probability equal to pNA (Kuechle,2009).

We are particularly interested in the agglomeration equilibria to identify the conditions under which each region maydevelop idiosyncratic levels of entrepreneurial activity. To calculate the agglomeration equilibria of the system of differenceequations given by (5) we set �p1 = �p2 = 0, d = 1and require that p1 /= p2. This results in a system of two quadratic equationswith two sets of interchangeable solutions equal to

pAi , pA

j = {bω(2m − bε) ±√

[b2ω2(bε − 2m)2 − 4b(mC − bεω)(2m2 − mbε)]} : {2b(mC − bεω)} (i, j = 1, 2; i /= j) (6)

where ε = � − w > 0 represents the advantage of E over ∼E in the case of under entry and ω = w − (� − C) the advantage of ∼Eover E in the case of over entry. Consistent with the literature on increasing returns, the two agglomeration equilibria areinterchangeable, in the sense that early small events determine which region has the higher level of entrepreneurial activity(Arthur, 1989; Minniti, 2005).

To assess the dynamics of the interregional model, we perform a stability analysis following standard methods in Hofbauerand Sigmund (1998, pp. 119–121). According to the calculations, the non-agglomeration equilibrium pNA = [(� − w)/C] isstable if and only if m > 0.5(b/C)(� − w)(C − � + w).2 Under this condition, the agglomeration equilibria pA

1 and pA2 in (6) are

unstable. If, however, this inequality is not satisfied, namely if m < 0.5(b/C)(� − w)(C − � + w) then pNA is unstable and thetwo agglomeration equilibria are stable.

The important feature of the dynamic analysis is that both agglomeration and non-agglomeration equilibria cannot besimultaneously stable. Either the two regions are drawn to the same level of entrepreneurial activity or they are pushed todifferent steady states. Fig. 1 depicts the location of the equilibria for a particular configuration of parameters (� = 100, w = 70;C = 50 and b = 0.01) as a function of the migration rate m. One can observe that for a migration rate of 5% the two agglomerationequilibria are (pA1

1 = 0.77; pA12 = 0.37) and (pA2

1 = 0.37; pA22 = 0.77) whereas the non-agglomeration equilibrium, which holds

for m ≥ 0.06, is given by pNA = pNA1 = pNA

2 = 0.6.In line with the New Economic Geography, the present model is subject to catastrophic agglomeration. As long as the rate

of migration is higher than the given threshold both regions will evolve to the same proportion of entrepreneurs; however,when the level of m drops below this threshold, the regions will start developing idiosyncratic levels of entrepreneurialactivity. This threshold is defined by m* = 0.5(b/C)(� − w)(C − � + w) and equals 0.06 for the parameters used to plot Fig. 1.

2 For pNA1 = pNA

2 = [(� − w)/C] the Jacobian of the system (5) has a trace equal to T = −m and a determinant equal to D = 2m − (b/C)(� − w)(C − � + w).



Fig. 1. Equilibrium solutions for given parameters.

Further notice that this process is characterized by hysteresis, as the occupational fates of the regions will be shaped byinitial conditions and early events.

As explained earlier, when 0 ≤ d < 1 there is no analytical solution to the system of equations (5) and therefore, no for-mula similar to (6) for the agglomeration equilibria. However, to gain intuition one can plot these equations and find theirintersection points. After attempting several parametric configurations, we determined the presence of a large set of param-eters for which this system behaves like the system under d = 1, in the sense that one can identify the two interchangeableagglomeration equilibria in the range 0 ≤ [p1, p2] ≤ 1. The main condition is that d /= 0.

To assess the system (5) when d = 0, we use numerical methods to calculate the solutions for different sets of parameters.We observe that the only stable equilibrium is pNA = (� − w)/C according to which both regions converge to the same levelof entrepreneurial activity. This shows that diversity can emerge only if there is a positive probability of playing the gamewith an individual from the other region. For values of d sufficiently higher than 0 we confirm that the system has the sameproperties as the one in which d = 1.

Note that for m = 0 and d = 1, the only two stable equilibria, namely (p∗1 = 0, p∗

2 = 1) and (p∗∗1 = 1, p∗∗

2 = 0), have bothregions fully specializing in a different occupation. This extreme outcome is possible because individuals play the marketentry game with an individual located in the other region (d = 1). In general, the concentration of economic activities amountsto some form of specialization, a phenomenon that is feasible only if regions engage in economic exchange. As our modeldeals with occupational choice instead of production decisions, specialization translates into idiosyncratic levels of entryand paid employment. Finally, note that in the absence of migration and economic interaction (d = 0, m = 0) two similarlyendowed regions will display the same amount of entrepreneurial activity as they will operate in autarky.

3.5. The persistence of agglomerations

In this section, we explore the impact of the different parameters of the model upon the stability of the agglomerationequilibria to assess the extent to which we can expect agglomeration to prevail in the long run. As stated in the previoussection, we expect agglomerations to emerge and persist when m < 0.5(b/C)(� − w)(C − � + w). This implies that the param-eters that increase the right-hand side of the equation or reduce the left hand, have the effect of raising the chances foragglomerations to emerge. By the same token, parameters that lower the right-hand side or increase the left-hand sidefoster regional equality.

We begin the analysis with the migration rate (m). Although social ties and financial resources constrain spatial mobility,empirical evidence shows that non-negligible rates of domestic migration tend to remain considerably stable over longperiods of time. In our model, high migration rates increase the left-hand side of the previous inequality and will thereforeact against the emergence of entrepreneurial agglomerations. To understand the reason for this occurring, it must be recalledthat when m = 0 and d = 1 the regions fully specialize in one occupation. As explained in the previous section, one of the reasonsfor that outcome is that playing the market entry game with an individual located in the other region allows individualsto reap the benefits that entail when an entrepreneur meets an individual who chooses paid employment. But that canonly happen if, in addition, individuals do not migrate. This is because migration is a compensating mechanism as far asthe number of entrepreneurs in each region is concerned. According to the last term of equations (5), exogenous migrationswaps entrepreneurs from the region with high levels of entrepreneurship to the region having low levels, undermining thediversity fostered by economic exchange. This effect however, is weakened if we incorporate success-biased migration, amechanism that reinforces diversity between the regions (see Eqs. (12) in the Appendix).

To understand this dynamics, assume that in addition to switching between occupations in response to the past income,individuals migrate towards the region with a higher expected payoff, given the amount of entry of the previous period.As the region with the higher level of entrepreneurship is the one having the higher expected income, entrepreneurial



Fig. 2. Case in which profit increases the agglomeration threshold.

concentrations will attract even more entrepreneurs, fostering a positive reinforcement mechanism characteristic of modelswith strategic complementarities.3 The final effect of migration on entrepreneurial agglomerations will depend upon therelative strength of these two forces. The merit of our model is that it is capable of elucidating the impact of two empiricallymeaningful mechanisms through which migration may affect concentrations.4 In light of this fact, we conclude that evenwhen exogenous migration works against the concentration of entrepreneurial activities, agglomerations are compatiblewith empirically meaningful migration rates.

The returns to entrepreneurship depend on two parameters, namely, profit (�) and the costs of competition (C). We startby considering the effects of � on the agglomeration threshold m*. An increase in � always improves the relative perfor-mance of entrepreneurship over paid employment as well as the autarkic rate of entrepreneurship pNA = (� − w)/C. However,it need not increase the likelihood of agglomeration via higher m*. Taking the derivative of m* = 0.5(b/C)(� − w)(C − � + w)with respect to �, we observe that this derivative is positive as long as � − w < C − � + w, a condition equivalent topNA = [(� − w)/C] < 0.5. The migration threshold reaches the maximum when � − w = C − � + w (at which point pNA = 0.5) anddecreases thereafter.5 To understand this relationship, consider that � − w represents the advantage of entrepreneurshipover paid employment when playing with an individual who chooses not to enter the market, whereas C − � + w representsthe relative advantage of paid employment when facing an entrepreneur. While the first one increases with higher values of�, the second decreases. If the players had interacted with the whole population and the capacity of the market was set at amore realistic level, these two terms would respectively represent the benefit to entry before the capacity is reached (underentry) and the cost of entry when this capacity had been surpassed (over entry). An increase in profit leads to a higher m*as long as the opportunity cost of over entry outweighs the advantage of entering the market before it reaches its capacity.Increases in profit beyond the point where � = w + C/2 diminish m*. To sum up, the further away pNA = (� − w)/C is from 0.5,the lower the rate of migration that is compatible with agglomerations. Migration balances out differences in the rates ofentrepreneurship in the regions and this process is stronger the closer pNA is to either 0 or 1.

As for the effect of changes in profit on the regional rates of entrepreneurship, Fig. 2 summarizes all the possible scenarios.An increase in profit, starting from a situation in which (� − w)/C < 0.5, (or � − w < C − � + w) increases the agglomer-

ation threshold from m0* to m1*. If the regions already possessed different rates of entrepreneurship (for instance at m)increases in profit would retain the diversity between the regions. If on the other hand the regions began with equal levelsof entrepreneurship (for instance at m′) a change in profit would set the regions onto new dynamic paths towards diversity.The region that initially gets ahead of the other will reinforce its advantage and evolve to a higher rate of entrepreneurship.

Fig. 3 shows the impact of � on m* for � − w > C − � + w. After an increase in profit, the regions may retain their diversity;however, if they start at a point such as m, the dynamics will force them to converge to the new autarkic equilibrium pNA = 0.6eliminating the original diversity. Finally, if � − w = C − � + w the agglomeration threshold will remain unchanged and bothregions will increase their level of entrepreneurial activity.

Wages have the opposite effect upon regional diversity than profits for a given set of parameters. The derivative of theright-hand side of the inequality m < 0.5(b/C)(� − w)(C − � + w) with respect to w is positive if and only if � − w > C − � + w(i.e., pNA > 0.5) and negative otherwise. This means that a wage increase will promote persistent agglomerations when therelative advantage of entrepreneurship is larger than the relative advantage of paid employment. The earlier analysis ofFigs. 2 and 3 applies to this case as well if we consider that the effect of an increase in profit is similar to a wage decrease.

3 As explained in the Appendix, this relationship ceases to hold true if d = 0. See the Appendix for further details.4 We thank one of he reviewers for suggesting this expansion of the model.5 Recall that for this game to be well defined, � < C + w.



Fig. 3. Case in which profit decreases the agglomeration threshold.

Fig. 4. The effect of competition costs.

The cost of competition, C, has an unambiguous effect upon the tendency to evolve idiosyncratic levels of entrepreneurshipand paid employment. The derivative of the right-hand side of equation m < 0.5(b/C)(� − w)(C − � + w) with respect to C isalways positive. This means that the increases in the costs of competition, and hence the efficiency loss due to unsuccessfulcoordination, induce regions towards regional divergence, as shown in Fig. 4. This is because the diversity allows the regionsto exploit the advantages of specialization, which increase with C.

The parameter measuring the strength of social learning, namely b, also exerts an unequivocal effect upon the stabilityof agglomerations. Increases in b have a stabilizing effect upon the tendency to concentrate. It must be recalled that bstrengthens the responsiveness of behaviors to observed payoff differences. After an individual is matched at random withanother to compare payoffs, two basic scenarios are feasible. First, both players choose the same strategy, so that nobodyswitches. Second, they choose differently, so that the player with the lower payoff increases her chances of switching tothe alternative strategy, with a strength that positively depends on b. From a psychological perspective, b = 0 representsa situation in which the individuals are completely indifferent towards the fate of the other individuals and b = 1/(� − w),a situation in which they are fully influenced. Higher values of b promote agglomerations of entrepreneurial activities byreinforcing choices that lead to higher expected payoffs. Success-biased migration (see the Appendix) has the same effect,and for the same reason.

Finally, if we assume 0 < d < 1, so that the individuals interact with other individuals in both regions, the agglomerationthreshold is given by m* = 0.5 (2d − 1)(b/C)(� − w)(C − � + w). As 2d − 1 < 1, the presence of d < 1 has the effect of decreasingthe range of conditions leading to regional diversity compared to the case in which d = 1. The higher rates of economicinteraction between the regions increase the likelihood of stable agglomeration as they offer the possibility of specialization.This provides another example of how interactions between regions, and more generally openness, may constitute a sourceof agglomeration economies (Matsuyama, 2002).



Fig. 5. The effect of success-biased learning.

4. The efficiency of the global economy

We have discussed the scenarios leading to multiple equilibria and their stability and showed that persistent regionaldivergence can occur in the presence of migration and when regions have similar economic potentials. We have so far notcommented on the efficiency consequences of such dynamics. In this section we analyze the total population payoffs underdifferent equilibrium configurations.

To accomplish this we calculate the equilibrium payoffs of both occupations in each region. The equilibrium payoff inregion i (Ii) is the sum of the expected payoff of each occupation weighted by their equilibrium frequencies in the region. Inother words,

I1(p∗1, p∗

2) = p∗1IE

1 + (1 − p∗1)I∼E

1

I2(p∗1, p∗

2) = p∗2IE

2 + (1 − p∗2)I∼E

2

(7)

To obtain the payoff for the whole economy, we add up these two payoffs. This results in

I(p∗1, p∗

2) = I1(p∗1, p∗

2) + I2(p∗1, p∗

2) = (2 − p∗1 − p∗

2)w + p∗1(� − Cp∗

1) + p∗2(� − Cp∗

2). (8)

The highest global payoff, � + w, occurs when regions fully specialize, i.e. when either p∗1 = 0 and p∗

2 = 1 or p∗1 = 1 and

p∗2 = 0. However, this state is evolutionary stable only when m = 0. We have observed that if the agglomeration equilibrium

is unstable, then the frequency of entrepreneurs in both regions is given by pNA1 = pNA

2 = pNA = [(� − w)/C]. In this situationI([(� − w)/C], [(� − w)/C]) = 2w, reflecting the fact that if regions evolve to the same level of entrepreneurial activity, eachearns on average w. An equilibrium is reached only when no individual has incentives to change her behavior and this canbe achieved only if both the entrepreneurs and employees expect, on average, the same earnings. In autarky there are nogains from specialization, and therefore, the income of each region can, at most, be w.

If on the other hand, the system evolves to any of the interchangeable agglomeration equilibria, the income of the globaleconomy is given by

I(pA1, pA

2) = {2bw[b(� − w − C)(� − w) + mC)] + [b(� − w) − 2m][b(� − w)(� − w − C) + 2mC]}{b[b(� − w)(� − w − C) + mC]} , (9)

which is higher than the total payoff under autarky (2w) but lower than the total payoff under full specialization (w + �).By means of Eqs. (1), (7) and (8) we obtain the general expression of global income:

I(p∗1, p∗

2) = 2w + (p∗1 + p∗

2)(� − w) − C[(

p∗21 + p∗2

2 ) + d(p∗1 − p∗

2

)2]. (10)

As expected, �, w, and C have unequivocal effects on global income. Higher profits and wages and lower competitioncosts increase the global income. The same holds true for d, because it allows regions to become specialized in one of thetwo occupations. The effect of d on the regional income depends on their relative rates of entrepreneurship. If p∗

1 > p∗2,

entrepreneurs in region 1 will benefit from the increased interaction with individuals in the other region, given that theoverall likelihood of over entry will be lesser for them. The opposite effect, although to a lesser extent, occurs in region 2,which has a lower rate of entrepreneurship.

As for the ex-post effect of success-biased social learning b on earnings, we have first calculated the effect of b on p∗1 and

p∗2. The numerical calculations are plotted in Fig. 5.

Starting from a given agglomeration equilibrium and assuming d = 1, increases in the value of b pull the values of p∗1 and p∗

2apart. The higher values of b increase the global and regional incomes although they affect the earnings of the entrepreneursand employees differently. The region that becomes more entrepreneurial (in this case, region 2) has a greater increase in



income. Entrepreneurs in that region earn higher payoffs in equilibrium because under the assumption of d = 1 they arematched with individuals in the other region. Entrepreneurs in the other region experience the opposite effect. Employeesin region 1 are better off compared with those who choose paid employment in region 2.

5. Conclusion

No single model can probably capture the emergence and persistence of every pattern of co-location. However, there isconsensus regarding the fundamental forces at the heart of this phenomenon. According to the literature, the key drivingforces are the widespread existence of increasing returns to scale and scope, and the positive complementarities arisingfrom the economic and social interactions (Glaeser et al., 2010a; Krugman, 1991b).

Consistent with the literature on entrepreneurial agglomerations (Forslid and Ottaviano, 2003; Glaeser et al., 2010a,b;Minniti, 2005; Strange, 2009) we have adopted an evolutionary game theoretic perspective capable of accommodating indi-vidual decision making, multiple equilibria, and economic exchange between regions. Our paper complements the literatureby analyzing a market entry game, and therefore, a situation in which the adoption of entrepreneurship is not positivelyreinforced. Concomitantly, we consider interactions between equally skilled individuals, while allowing for migration andsuccess-driven social learning.

We contribute to the literature on microfoundations of agglomerations economies (Forslid and Ottaviano, 2003; Strange,2009) by providing a novel mechanism by which two regions may evolve idiosyncratic levels of entrepreneurial activity. Forthis mechanism to act, it is necessary that individuals from different regions compete to enter the same market. This type ofeconomic interaction allows for regional specialization, a process that in the presence of success-biased choices concerningoccupation and location will drive regions to develop different rates of entrepreneurship.

The model has two agglomeration equilibria and one non-agglomeration equilibrium. The agglomeration equilibria areinterchangeable in the sense that early events will determine which region has the higher level of entrepreneurial activity.A crucial feature is that both types of equilibria cannot be simultaneously stable. There are some forces that encourage andothers that discourage agglomerations. Economic interaction and success biased learning foster agglomerations whereasexogenous migration acts against it. Profits and wages have the opposite effects upon the stability of agglomerations for agiven set of parameters. Higher profits foster agglomerations when the opportunity cost of entering the market is higherthan the opportunity cost of staying out. Increases in wages foster agglomerations in the opposite situation. Competitioncosts or the existence of a market capacity, always favor the emergence of diversity, as they increase the advantages ofspecialization.

Regarding the limitations of the model and the generality of the results, it should be mentioned that in our model theregions are exogenously located and that their relative distance does not affect choices. Nevertheless, two comments arein place. First, the regions need to be separated in space or otherwise so that the two markets do not collapse into one. Inthat scenario, the autarkic solution would prevail, eliminating the possibility of diverse rates of entrepreneurship. Second,the parameters representing the economic and social interaction (d and b) could be taken to account for constraints to theeconomic and cultural exchange such as distance. As we expect d and b to be higher for closer regions, we can infer thatthe distance between the regions hinders the emergence of agglomerations. Finally, we should also acknowledge that entry,even if relevant, is only one aspect of the entrepreneurial phenomenon. Market entry games assume that a market alreadyexists and fail to provide a proper analysis of disruptive innovations, a situation that is best modeled by other frameworksof decision making. This development warrants further research.

Agglomeration phenomena involve complex processes and dynamic interdependencies that merit careful examinationin order to build a theory of spatial distribution of economic activities. In line with the New Economic Geography andrecent research on cultural evolution, our model supports the view that regional divergence need not be the consequence ofintrinsic heterogeneity but emerges as the outcome of the cumulative processes of the interactions between homogeneouspopulations. In this regard, our model unveils a fundamental mechanism underlying the emergence of diversity.

Last but not least, the model has implications for policy making. Even when, as we have demonstrated, agglomerationsenhance the performance of the whole economy, changes in the value of the parameters could induce unintended shiftsbetween agglomeration and non-agglomeration equilibria or no change at all.

Acknowledgements

We are grateful two anonymous reviewers for suggestions that have significantly improved this manuscript. The usualdisclaimer applies.

Appendix A. Success biased migration

To account for the economically motivated immigration, in this section we assume a rate of migration from region i toregion j equal to m[1 + a (Ij − Ii)], where Ii = piI

Ei

+ (1 − pi)I∼Ei

is the expected income in region i (i = 1, 2). The coefficient a > 0measures the responsiveness of the individuals to the income expected if they migrate to the other region. If a = 0, thenmigration is only due to exogenous factors as before.



The resulting equations for the one-step change in p1 and p2 provided d = 1 are given by

�p1 = p1(1 − p1)b(IE1 − I∼E

1 ) + mp2[1 + a(I1 − I2)] − mp1[1 + a(I2 − I1)]

�p2 = p2(1 − p2)b(IE2 − I∼E

2 ) + mp1[1 + a(I2 − I1)] − mp2[1 + a(I1 − I2)](11)

The second term represents the inflow of individuals into a region while the third refers to the outflow. Note thatI1 − I2 = (� − w) (p1 − p2) so that the region with the higher rate of entrepreneurship has a higher expected income. Thisis not necessarily the case if d = 0, namely if individuals interact only with others in their region. In this case, the higherrates of entrepreneurship lead to higher income only if the combined rates of entry of the regions is relatively small so that[(� − w)/C] > p1 + p2.

Substituting I1 and I2 by the formula given above, IEi

and I∼Ei

by their definitions in Section 3 and assuming that d = 1 weobtain

�p1 = p1(1 − p1)b( ̆ − p2C − w) + m(p2 − p1)[1 − a(p2 + p1)(� − w)]

�p2 = p2(1 − p2)b( ̆ − p1C − w) + m(p1 − p2)[1 − a(p2 + p1)(� − w)](12)

This system of dynamic recursions cannot be solved analytically. Therefore, we lack expressions for the agglomerationequilibria that are not corner solutions. However, it can be observed that this dynamic system shares a subset of the solutionsof the system that results when a = 0, namely (p∗

1 = 0, p∗2 = 1), (p∗

1 = 1, p∗2 = 0) and the non-agglomeration equilibria

pNA1 = pNA

2 = pNA = [(� − w)/C].The assumption of success-biased migration increases the likelihood of agglomeration equilibria. First note that when

a = 0 and p2 > p1, m helps to balance the rate of entrepreneurship between the regions through an increment in p1. Theassumption of success biased learning (a > 0) on the other hand reinforces the differences between the regions, because aand �p1 are negatively correlated. This implies that a > 0 has the effect of making stable agglomerations more likely. Thesame conclusion can be drawn by the examination of the Jacobian of the system (12) at the autarkic equilibrium pNA

1 = pNA2 =

pNA = [(� − w)/C]. Whereas the determinant is always positive the sign of the trace depends upon the importance of thesuccess-biased migration. There is a threshold beyond which this equilibrium becomes unstable, as given by C/2(� − w)2.The autarkic equilibrium is stable only when a < C/2(� − w)2; however, even in that case, its presence increases the rangeof migration m conducive to agglomeration. Therefore, the assumption of a = 0 restricts the conditions leading to stableagglomerations.

As explained in Section 3.2, m represents the extent to which the exogenous forces influence migration. Success-biasedmigration on the other hand, fully endogenizes the choice of location. Ideally, the process of migration should consider bothexogenous and endogenous causes as is done in this section.

Appendix B. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jebo.2014.03.017.

References

Acemoglu, D., 2009. Introduction to Modern Economic Growth. Princeton University Press, Princeton.Acs, Z.J., Audretsch, D.B., 2005. Entrepreneurship, innovation and technological change. Found. Trends Entrepreneurship 1 (4), 1–49.Acs, Z.J., Audretsch, D.B., Feldman, M.P., 1992. Real effects of academic research. Am. Econ. Rev. 82 (1), 363–367.Acs, Z.J., Malecki, E., 2003. Entrepreneurship in Rural America: the big picture. In: Drabenstott, M., Novack, N., Abraham, B. (Eds.), Main Streets of Tomorrow:

Growing and Financing Rural Entrepreneur: A Conference Summary. Federal Reserve Bank, Center for the Study of Rural America, Kansas City, pp. 21–29.Acs, Z.J., Mueller, P., 2008. Employment effects of business dynamics: mice, gazelles and elephants. Small Bus. Econ. 30, 85–100.Acs, Z.J., Varga, A., 2005. Entrepreneurship, agglomeration and technological change. Small Bus. Econ. 24, 323–334.Aldrich, H.E., 1979. Organizations and Environments. Englewood Cliffs, NJ, Prentice Hall.Aldrich, H.R., Zimmer, C., 1986. Entrepreneurship through social networks. In: Sexton, D., Smilor, R. (Eds.), The Art and Science of Entrepreneurship.

Cambridge, Ballinger.Andersson, M., Koster, S., 2010. Sources of persistence in regional start-up rates –evidence from Sweden. J. Econ. Geogr. 11, 179–201.Anselin, L., Varga, A., Acs, Z.J., 1997. Local geographic spillovers between university research and high technology innovations. J. Urban Econ. 42, 422–448.Armington, C., Acs, Z., 2002. The determinants of region variation in new firm formation. Reg. Stud. 36 (1), 33–45.Arthur, B., 1994. Increasing Returns and Path Dependence in the Economy. The University of Michigan Press, Ann Arbor.Arthur, B., 1989. Competing technologies, increasing returns, and lock-in by historical events. Econ. J. 99, 116–131.Audretsch, D.B., Feldman, M.P., 1996. R&D spillovers and the geography of innovation and production. Am. Econ. Rev. 86, 630–640.Audretsch, D.B., Lehmann, E., 2005. Does the knowledge spillover theory of entrepreneurship hold for regions? Res. Policy 34 (8), 1191–1202.Commendatore, P., Currie, M., Kubin, I., 2008. Footloose entrepreneurs, taxes and subsidies. Spatial Econ. Anal. 3, 115–141.Commendatore, P.M., Kubin, I., 2013. A 3-regions new economic geography model in discrete time. Global Anal. Dyn. Models Econ. Finance, 159–184.Cooper, A., Folta, T., 2000. Entrepreneurship and high technology clusters. In: Sexton, D., Landström, H. (Eds.), The Blackwell Handbook of Entrepreneurship.

Blackwell Publishers Ltd, Oxford, pp. 348–367.Currie, M., Kubin, I., 2006. Chaos in the core-periphery model. J. Econ. Behavior Org. 60, 252–275.Dahl, M., Sorenson, O., 2010. The migration of technical workers. J. Urban Econ. 67 (1), 33–45.Dosi, G., 1997. Opportunities, incentives and the collective patterns of technological change. Econ. J. 107, 1530–1547.Doms, M., Lewis, E., Robb, A., 2010. Local labor force education, new business characteristics, and firm performance. J. Urban Econ. 67 (1), 61–77.Duranton, G., Puga, D., 2004. Micro-foundations of urban agglomeration economies. In: Henderson, J.V., Thisse, J.-F. (Eds.), Handbook of Urban and Regional

Economics, vol. 4. Elsevier, Amsterdam, pp. 2063–2118.



Ellison, G., Glaeser, E.L., 1997. Concentration in U.S. manufacturing industries: a dartboard approach. J. Polit. Econ. 105 (5), 889–927.Ellison, G., Glaeser, E.L., Kerr, W., 2010. What causes industry agglomeration? Evidence from coagglomeration patterns. Am. Econ. Rev. 100 (3), 1195–1213.Ellison, G., Glaeser, E.L., 1999. The geographic concentration of industry: does natural advantage explain agglomeration? Papers and Proceedings. Am. Econ.

Rev. 89, 311–316.Feldman, M.P., 1993. An examination of the geography of innovation. Ind. Corp. Change 2, 451–470.Fritsch, M., Wyrwich, M., (Discussion Paper 1224) 2012. The long persistence of regional entrepreneurship culture: Germany 1925–2005. Deutsches Institut

für Wirtschaftsforschung.Fritsch, M., Mueller, P., 2007. The persistence of regional new business formation activity over time – assessing the potential of policy promotion programs.

J. Evol. Econ. 17, 299–315.Forslid, R., Ottaviano, G.I.P., 2003. An analytically solvable core-periphery model. J. Econ. Geogr. 3, 229–240.Fujita, M., Krugman, P., Venables, A.J., 1999. The Spatial Economy: Cities, Regions and International Trade. MIT Press, Cambridge.Glaeser, E.L., Kerr, W.R., Ponzetto, G.A.M., 2010a. Clusters of entrepreneurship. J. Urban Econ. 67 (1), 150–168.Glaeser, E.L., Rosenthal, S.S., Strange, W.C., 2010b. Urban economics and entrepreneurship. J. Urban Econ. 67 (1), 1–14.Gordon, I.R., McCann, P., 2000. Industrial clusters: complexes, agglomeration and/or social networks? Urban Stud. 37 (3), 513–532.Granovetter, M., 1985. Economic action and social structure: the problem of embeddedness. Am. J. Sociol. 91, 480–510.Henrich, J., Boyd, R., 2008. Division of labor, economic specialization and the evolution of social stratification. Curr. Anthropol. 49, 715–724.Hofbauer, J., Sigmund, K., 1998. Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge, UK.Jaffe, A., Trajtenberg, M., Henderson, R., 1993. Geographic localization of knowledge spillovers as evidenced by patent citations. Q. J. Econ. 63, 577–598.Kerr, W., 2010. Breakthrough inventions and migrating clusters of innovation. J. Urban Econ. 67 (1), 46–60.Kim, P.H., Aldrich, H.E., 2005. Social capital and entrepreneurship. Found. Trends Entrepreneurship 1 (2), 1–52.Klepper, S., 2007. Disagreements, spinoffs, and the evolution of Detroit as the capital of the U.S. automobile industry. Manage. Sci. 53 (4), 616–631.Klepper, S., 2010. The origin and growth of industry clusters: the making of Silicon Valley and Detroit. J. Urban Econ. 67, 15–32.Krugman, P., 1991a. Increasing returns and economic geography. J. Polit. Econ. 99, 483–499.Krugman, P., 1991b. Geography and Trade. Leuven University Press/MIT Press, Leuven/Cambridge, MA, London, England.Kuechle, G., 2009. Heterogeneity and persistence in entrepreneurship: an evolutionary game theoretic approach. J. Bus. Venturing 26 (4), 458–471.Leppälä, S., Desrochers, P., 2010. The division of labor need not imply regional specialization. J. Econ. Behav. Org. 74, 137–147.Marshall, A., 1920. Principles of Economics. McMillan, London.McElreath, R., Boyd, R., 2007. Mathematical Models of Social Evolution: A Guide for the Perplexed. University of Chicago Press, Chicago.Matsuyama, K., 2002. Explaining Diversity: Symmetry-Breaking in Complementarity Games. Am. Econ. Rev. 92, 241–246.Minniti, M., 2005. Entrepreneurship and network externalities. J. Econ. Behav. Org. 57, 1–27.Neary, P.J., 2001. Of hype and hyperbolas: Introducing the New Economic Geography. J. Econ Lit. 39 (2), 536–561.Orsenigo, L., 2006. Clusters and clustering: stylized facts, issues, and theories. In: Braunerhjelm, P., Feldman, M. (Eds.), Cluster Genesis: Technology-Based

Industrial Development. Oxford University Press, Oxford.Parker, S., 2009. The Economics of Entrepreneurship. Cambridge University Press, Cambridge.Reynolds, P.D., Miller, B., Maki, W., 1995. Explaining regional variation in business births and deaths: U.S. 1976–1988. Small Bus. Econ. 7, 389–407.Richerson, P., Boyd, R., 2005. Not By Genes Alone: How Culture Transformed Human Evolution. University of Chicago Press, Chicago.Saxenian, A., 1994. Regional Advantage: Culture and Competition in Silicon Valley and Route 128. Cambridge University Press, Cambridge, MA.Selten, R., Güth, W., 1982. Equilibrium point selection in a class of market entry games. In: Diestler, M., Furst, E., Schwadiauer, G. (Eds.), Equilibrium Point

Selection in a Class of Market Entry Games. Physica-Verlag, Wien-Wurzburg.Strange, W.C., 2009. Agglomeration research in the age of disaggregation. Can. J. Econ. 42 (1), 1–27.Stuart, T., Sorenson, O., 2003. The geography of opportunity: spatial heterogeneity in founding rates and the performance of biotechnology firms. Res. Policy

32, 229–253.Thornton, P.H., Flynn, K.H., 2003. Entrepreneurship, networks, and geographies. In: Acs, Z.J., Audretsch, D.B. (Eds.), Handbook of Entrepreneurship Research.

Kluwer Academic Publishers, pp. 401–433.U.S. Census Bureau Geographic mobility, 1947–2008. Retrieved from http://www.census.gov/population/www/socdemo/migrate.html#census

Regional concentration of entrepreneurial activities

Documents

Transcript of Regional concentration of entrepreneurial activities