
on Game Theory 
By:  Martin Kaae Jensen; Alexandros Rigos 
Abstract:  This paper introduces two new concepts in evolutionary game theory: Nash equilibrium with Group Selection (NEGS) and Evolutionarily Stable Strategy with Group Selection (ESSGS). These concepts generalize Maynard Smith and Price (1973) to settings with arbitrary matching rules, inparticular they reduce, respectively, to Nash equilibrium and ESS when matching is random. NEGS and ESSGS are to the canonical group selection model of evolutionary theory what Nash Equilibrium and ESS are to the standard replicator dynamics: any NEGS is a steady state, any stable steady state is a NEGS, and any ESSGS is asymptotically stable. We exploit this to prove what may be called “the second welfare theorem of evolution”: Any evolutionary optimum will be a NEGS under some matching rule. Our results are illustrated in HawkDove, Prisoners’ dilemma, and Stag Hunt games. 
Keywords:  Evolutionary Game Theory, Evolutionarily Stable Strategy, ESS, Group Selection, Nonrandom Matching, Traitgroup Model, Haystack Model. 
JEL:  C72 C73 
Date:  2014–07 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:14/09&r=gth 
By:  Britz V.; Herings P.J.J.; Predtetchinski A. (GSBE) 
Abstract:  We consider a class of perfect information unanimity bargaining games, where the players have to choose a payoff vector from a fixed set of feasible payoffs. The proposer and the order of the responding players is determined by a state that evolves stochastically over time. The probability distribution of the state in the next period is determined jointly by the current state and the identity of the player who rejects the current proposal.This protocol encompasses a vast number of special cases studied in the literature. These special cases have in common that equilibria in pure stationary strategies exist, are efficient, are characterized by the absence of delay, and converge to a unique limit corresponding to an asymmetric Nash bargaining solution. For our more general protocol, we show that subgame perfect equilibria in pure stationary strategies need not exist. When such equilibria do exist, they may exhibit delay. Limit equilibria as the players become infinitely patient need not be unique. 
Keywords:  Bargaining Theory; Matching Theory; 
JEL:  C78 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:unm:umagsb:2014019&r=gth 
By:  Irit Nowik; Shmuel Zamir 
Abstract:  The purpose of this work is to offer for any zerosum game with a unique strictly mixed Nash equilibrium, a measure for the risk when deviating from the Nash equilibrium. We present two approaches regarding the nature of deviations; strategic and erroneous. Accordingly, we define two models. In each model we define risk measures for the rowplayer (PI) and the column player (PII), and prove that the risks of PI and PII coincide. This result holds for any norm we use for the size of deviations. We develop explicit expressions for the risk measures in the L1 and L2 norms, and compute it for several games. Although the results hold for all norms, we show that only the L1 norm is suitable in our context, as it is the only norm which is consistent in the sense that it gives the same size to potentially equivalent deviations. The risk measures defined here enables testing and evaluating predictions on the behavior of players. For example: Do players deviate more in a game with lower risks than in a game with higher risk? 
Date:  2014–04 
URL:  http://d.repec.org/n?u=RePEc:huj:dispap:dp664&r=gth 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Tibor Heumann (Dept. of Economics, Yale University); Stephen Morris (Dept. of Economics, Princeton University) 
Abstract:  In an economy of interacting agents with both idiosyncratic and aggregate shocks, we examine how the information structure determines aggregate volatility. We show that the maximal aggregate volatility is attained in a noise free information structure in which the agents confound idiosyncratic and common components of the payoff state, and display excess response to the common component, as in Lucas (1972). The upper bound on aggregate volatility is linearly increasing in the variance of idiosyncratic shocks, for any given variance of aggregate shocks. Our results hold in a setting of symmetric agents with linear best responses and normal uncertainty. We show our results by providing a characterization of the set of all joint distributions over actions and states that can arise in equilibrium under any information structure. This tractable characterization, extending results in Bergemann and Morris (2013b), can be used to address a wide variety of questions. 
Keywords:  Incomplete information, Bayes correlated equilibrium, Volatility, Moments restrictions, Linear best responses, Quadratic payoffs 
JEL:  C72 C73 D43 D83 
Date:  2013–12 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1928r&r=gth 
By:  Alexander Matros (Darla Moore School of Business, University of South Carolina); Alex Possajennikov (Department of Economics, University of Nottingham) 
Abstract:  We consider mechanisms for allocating a commonvalue prize between two players in an incomplete information setting. In this setting, each player receives an independent private signal about the prize value. The signals are from a discrete distribution and the value is increasing in both signals. First, we characterize symmetric equilibria in four mechanisms: a lottery; and Â…rstprice, secondprice, and allpay auctions. Second, we establish revenue equivalence of these auction mechanisms in this setting. Third, we describe conditions under which the expected revenue is higher in the lottery than in any of the auctions. Finally, we identify an optimal mechanism and its implementation by means of reserve prices in lottery and auction mechanisms. 
Keywords:  common value; contests; auctions 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201407&r=gth 
By:  Michael D. Carr; Phil Mellizo 
Abstract:  Data from lab experiments support the claim that individuals have social preferences. Most models of social preferences, however, consider only the distribution of outcomes, not the source of the endowment used in the game. Once the source is considered, outcomes in the ultimatum game are more difficult to interpret. We extend the ultimatum game to allow for responderproduced endowments. We find that offers increase when the responder produces the endowment, but rejection rates are lower. Further, offers remain below 100% of the endowment, suggesting that unproductive proposers feel entitled to a part of the endowment, and responders respect this right. 
JEL:  C91 D30 D63 
Date:  2013–09 
URL:  http://d.repec.org/n?u=RePEc:mab:wpaper:2013_01&r=gth 
By:  Andrew McLennan (School of Economics, The University of Queensland) 
Abstract:  The effect of perturbing a parameterâ€”comparative staticsâ€”is, of course, a familiar and important issue in economic analysis. Perfection of a single Nash equilibrium (Selten (1975)) is defined by requiring that at least some perturbations in a given class give rise to perturbed games that have nearby equilibria. Roughly, Kohlberg and Mertens (1986) define strategic stability of a set of equilibria by requiring that for all sufficiently small perturbations, the perturbed games have equilibria near the set. This note presents a topological result concerning the behavior of such nearby equilibria when there is a function from a neighborhood of the relevant set of equilibria to the space of perturbations. 
Date:  2014–07–21 
URL:  http://d.repec.org/n?u=RePEc:qld:uq2004:526&r=gth 
By:  Nicolas Jacquemet (EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris, BETA  Bureau d'économie théorique et appliquée  CNRS : UMR7522  Université de Strasbourg  Université Nancy II); Adam Zylbersztejn (EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris, CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne) 
Abstract:  Experiments based on the Beard and Beil (1994) twoplayer coordination game robustly show that coordination failures arise as a result of two puzzling behaviors: (i) subjects are not willing to rely on others' selfinterested maximization, and (ii) selfinterested maximization is not ubiquitous. Such behavior is often considered to challenge the relevance of subgame perfectness as an equilibrium selection criterion, since weakly dominated strategies are actually used. We report on new experiments investigating whether inequality in payoffs between players, maintained in most lab implementations of this game, drives such behavior. Our data clearly show that the failure to maximize personal payoffs, as well as the fear that others might act this way, do not stem from inequality aversion. This result is robust to varying the saliency of decisions, repetitionbased learning and cultural differences between France and Poland. 
Keywords:  Coordination Failure ; Subgame perfectness ; Noncredible threats; Laboratory experiments; Social Preferences; Inequality Aversion 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs01026080&r=gth 
By:  Michael Caldara (Economic Science Institute, Chapman University); Michael McBride (Department of Economics, University of CaliforniaIrvine) 
Abstract:  Many social and economic networks emerge among actors that only partially observe the network when forming network ties. We ask: what types of network architectures form when actors have limited observation, and does limited observation lead to less efficient structures? We report numerous results from a laboratory experiment that varies both network observation and the cost of forming links. Overall, we find that limited network observation does not inevitably lead to highly inefficient networks but instead might actually inhibit inefficient positional jockeying among actors. 
Keywords:  Networks; Limited observation; Coordination 
JEL:  C92 D83 D85 
Date:  2014–07 
URL:  http://d.repec.org/n?u=RePEc:irv:wpaper:141501&r=gth 