
on Game Theory 
Issue of 2011‒08‒09
fifteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Frank Riedel (Institute of Mathematical Economics, Bielefeld University); Linda Sass (Institute of Mathematical Economics, Bielefeld University) 
Abstract:  Ambiguity can be used as a strategic device in some situations. To demonstrate this, we propose and study a framework for normal form games where players can use Knightian uncertainty strategically. In such Ellsberg games, players may use Ellsberg urns in addition to the standard objective mixed strategies. We assume that players are ambiguityaverse in the sense of Gilboa and Schmeidler. While classical Nash equilibria remain equilibria in the new game, there arise new Ellsberg equilibria that can be quite different from Nash equilibria. A negotiation game with three players illustrates this finding. Another class of examples shows the use of ambiguity in mediation. We also highlight some conceptually interesting properties of Ellsberg equilibria in two person games with conflicting interests. 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:452&r=gth 
By:  Messaoud Deghdak (Laboratoire de Mathématiques Appliquées et Modélisation  Département de Mathématiques); Monique Florenzano (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasiconcave. Moreover, we study the continuity of Berge's strong equilibrium correspondence and prove that most of Berge's strong games are essential. 
Keywords:  Nash equilibrium, strong Berge equilibrium, fixed point, essential games. 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00611851&r=gth 
By:  Giovanna Devetag; Francesca Pancotto; Thomas Brenner 
Abstract:  In minority games, players in a group must decide at each round which of two available options to choose, knowing that only subjects who picked the minority option obtain a positive reward. Previous experiments on the minority and similar congestion games have shown that players interacting repeatedly are remarkably able to coordinate efficiently, despite not conforming to Nash equilibrium behavior. We conduct an experiment on a minorityofthree game in which each player is a team composed by three subjects. Each team can freely discuss its strategies in the game and decisions must be made via a majority rule. Team discussions are recorded and their content analyzed to detect evidence of strategy coevolution among teams playing together. Our main results of team discussion analysis show no evidence supporting the mixed strategy Nash equilibrium solution, and support a lowrationality, backwardlooking approach to model behavior in the game, more consistent with reinforcement learning models than with beliefbased models. Showing level2 rationality (i.e., reasoning about others' beliefs) is positively and significantly correlated with higher than average earnings in the game, showing that a mildly sophisticated approach pays off. In addition, teams that are more successful tend to become more egocentric over time, paying more attention to their own past successes than to the behavior of other teams. Finally, we find evidence of mutual adaptation over time, as teams that are more strategic (i.e., they pay more attention to other teams' moves) induce competing teams to be more egocentric instead. Our results contribute to the understanding of coordination dynamics resting on heterogeneity and coevolution of decision rules rather than on conformity to equilibrium behavior. In addition, they provide support at the decision process level to the validity of modeling behavior using lowrationality reinforcement learning models. 
Keywords:  coordination, minority game, market efficiency, information, selforganization, reinforcement learning 
JEL:  C72 C91 C92 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:trn:utwpce:1102&r=gth 
By:  Nicolas Jacquemet (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Adam Zylbersztejn (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  In experiments based on the Beard and Beil (1994) game, second movers very often fail to select the decision that maximizes both players payoff. This note reports on a new experimental treatment, in which we neutralize the potential effect of inequality aversion on the likelihood of this behavior. We show this behavior is robust to this change, even after allowing for repetitionbased learning. 
Keywords:  Coordination failure, laboratory experiments, aversion to inequality. 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00611696&r=gth 
By:  Celik, Gorkem; Peters, Michael 
Abstract:  We study an incomplete information game in which players are involved in a reciprocal relationship that allows them to coordinate their actions by contracting among themselves. We model this as a competing mechanism game in which players have the ability to write contracts. We characterize the set of outcome functions that can be supported as equilibrium in this enhanced game. We use our characterization to show that the set of supportable outcomes is bigger than the set of outcomes supported by a centralized mechanism designer who can offer mechanisms in which all players participate. The difference is that the contracting game makes it possible for players to convey partial information about their type at the time they offer contracts. 
Date:  2011–08–01 
URL:  http://d.repec.org/n?u=RePEc:ubc:pmicro:gorkem_celik201119&r=gth 
By:  Jacob K. Goeree; Alexey Kushnir 
Abstract:  We consider a standard social choice environment with linear utilities and independent, onedimensional, private values. We provide a short and constructive proof that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents. We demonstrate the usefulness and applicability of our approach with several examples. Finally, we show that the equivalence between Bayesian and dominant strategy implementation breaks down when utilities are nonlinear or when values are interdependent, multidimensional, or correlated. 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:021&r=gth 
By:  Andrea Collevecchio (Department of Management, Università Ca' Foscari Venezia); Marco LiCalzi (Department of Management, Università Ca' Foscari Venezia) 
Abstract:  We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a partition generated by a random scheme. Assuming that agents' partitions are independently and identically distributed, we prove that the asymptotic probability of nontrivial common knowledge undergoes a phase transition. Regardless of the number of agents, when their cognitive capacity is suciently large, the probability goes to one; and when it is small, it goes to zero. 
Keywords:  Common knowledge; Epistemic game theory; Random partitions 
JEL:  C72 D83 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:vnm:wpdman:6&r=gth 
By:  Fabrice Barthelemy; Mathieu Martin; Bertrand Tchantcho (THEMA, Universite de CergyPontoise; THEMA, Universite de CergyPontoise; University of Yaounde I, Ecole Normale Superieure, Cameroon, PO Box 47 Yaounde) 
Abstract:  The purpose of this paper is to present a structural specification of the Shapley Shubik and Banzhaf power indices in a weighted voting rule. We compare them in term of the cardinality of the sets of power vectors (PV). This is done in different situations where the quota or the number of seats are fixed or not. 
Keywords:  ShapleyShubik, Banzhaf, power index, power vectors. 
JEL:  C7 D7 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201114&r=gth 
By:  Christopher Reicher 
Abstract:  This paper documents the short run and long run behavior of the search and matching model with staggered Nash wage bargaining. It turns out that there is a strong tradeoff inherent in assuming that previously bargained sticky wages apply to new hires. If sticky wages apply to new hires, then the staggered Nash bargaining model can generate realistic volatility in labor input, but it predicts a strong counterfactually negative long run relationship between inflation and unemployment. This finding is robust to including a microeconomically realistic degree of indexation of wages to inflation. The lack of a negative long run relationship between trend inflation and unemployment provides indirect evidence against the proposed mechanism that high inflation systematically makes new hiring more profitable by depressing the real wages of new hires 
Keywords:  Sticky wages, staggered Nash bargaining, trend inflation, unemployment, search and matching 
JEL:  E24 E25 J23 J31 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:kie:kieliw:1722&r=gth 
By:  Güth, Werner; Pull, Kerstin; Stadler, Manfred 
Abstract:  We study strategic interfirm competition allowing for internal conflicts in each seller firm. Intrafirm conflicts are captured by a multiagent framework with principals implementing a revenue sharing scheme. For a given number of agents, interfirm competition leads to a higher revenue share for the agents, higher equilibrium effort levels and higher agent utility, but lower profits for the firms. The winners from antitrust policy are thus not only the consumers but also the agents employed by the competing firms.  
Keywords:  agency theory,strategic interfirm competition,revenue sharing 
JEL:  C72 L22 M52 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:zbw:tuewef:14&r=gth 
By:  Levent Celik; Bilgehan Karabay; John McLaren 
Abstract:  In democracies, trade policy is the result of interactions among many agents with different agendas. In accordance with this observation, we construct a dynamic model of legislative trade policymaking in the realm of distributive politics. An economy consists of different sectors, each of which is concentrated in one or more electoral districts. Each district is represented by a legislator in the Congress. Legislative process is modeled as a multilateral sequential bargaining game a la Baron and Ferejohn (1989). Some surprising results emerge: bargaining can be welfareworsening for all participants; legislators may vote for bills that make their constituents worse off; identical industries will receive very different levels of tariff. The results pose a challenge to empirical work, since equilibrium trade policy is a function not only of economic fundamentals but also of political variables at the time of congressional negotiations – some of them random realizations of mixed bargaining strategies. 
JEL:  C72 C78 D72 F13 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:17262&r=gth 
By:  Fabrice Barthelemy; Mathieu Martin (THEMA, Universite de CergyPontoise; THEMA, Universite de CergyPontoise) 
Abstract:  In this paper, we compare five wellknown methods of apportionment, the ones by Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the wellknown Banzhaf power index and the populations are the ones of the different States of the U.S. We first explain under which conditions this comparison makes sense. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results. 
Keywords:  Banzhaf index, methods of apportionment, distances, balance populationpower. 
JEL:  C7 D7 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201113&r=gth 
By:  Martin Shubik 
Date:  2011–07–31 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:786969000000000173&r=gth 
By:  Stark, Oded; Jakubek, Marcin 
Abstract:  This paper asks whether population growth is conducive to the sustainability of cooperation. A simple model is developed in which farmers who live around a circular lake engage in trade with their adjacent neighbors. The payoffs from this activity are governed by a prisoner's dilemma rule of engagement. Every farmer has one son when the population is not growing, or two sons when it is growing. In the former case, the son takes over the farm when his father dies. In the latter case, one son stays on his father's farm, whereas the other son settles around another lake, along with the other sons of the other farmers. During his childhood, each son observes the strategies and the payoffs of his father and of the trading partners of his father, and imitates the most successful strategy when starting farming on his own. Then mutant defectors are introduced into an allcooperator community. The defector strategy may spread. A comparison is drawn between the impact in terms of the sustainability of cooperation of the appearance of the mutants in a population that is not growing, and in one that is growing. It is shown that the exante probability of sustaining the cooperation strategy is higher for a community that is growing than for a stagnant community.  
Keywords:  Population growth,Imitation,Sustainability of cooperation 
JEL:  C72 D01 D83 J19 J62 R12 R23 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:zbw:tuewef:15&r=gth 
By:  Stadler, Manfred 
Abstract:  As is wellknown from the literature on oligopolistic competition with incomplete information, firms have an incentive to share private demand information. However, by assuming verifiability of demand data, these models ignore the possibility of strategic misinformation. We show that if firms can send misleading demand information, they will do so. Furthermore, we derive a costly signaling mechanism implementing demand revelation, even without verifiability. For the case of a gamma distribution of the firms' demand variables, we prove that the expected gross gains from information revelation exceed the expected cost of signaling if the skewness of the distribution is sufficiently large and the products are sufficiently differentiated.  
Keywords:  Information sharing,simultaneous signaling,demand uncertainty 
JEL:  C73 D82 L13 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:zbw:tuewef:17&r=gth 