
on Game Theory 
Issue of 2013‒04‒20
thirteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Herve Moulin; Indrajit Ray; Sonali Sen Gupta 
Abstract:  We consider a class of symmetric twoperson quadratic games where coarse correlated equilibria  CCE  (Moulin and Vial 1978) can strictly improve upon the Nash equilibrium payoffs, while correlated equilibrium  CE  (Aumann 1974, 1987) cannot, because these games are potential games. We compute the largest feasible total utility in any CCE in those games, and show that it is achieved by a CCE involving only two pure strategy profiles. Applications include the Cournot duopoly and the game of public good provision, where the improvement over and above the Nash equilibrium payoff can be substantial. 
Keywords:  Coarse correlated equilibrium, Quadratic games, Duopoly models, Public good 
JEL:  C72 
Date:  2013–03 
URL:  http://d.repec.org/n?u=RePEc:bir:birmec:1310&r=gth 
By:  Gagen, Michael 
Abstract:  This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same strategic situation. In particular, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the dimensionality and volume of the underlying probability parameter spaces. These differences arise as probability theory employs structure preserving isomorphic mappings when constructing strategy spaces to analyze games. In contrast, game theory uses weaker mappings which change some of the properties of the underlying probability distributions within the mixed strategy space. Here, we explore how using strong isomorphic mappings to define game strategy spaces can alter rational outcomes in simple games . Specific example games considered are the chain store paradox, the trust game, the ultimatum game, the public goods game, the centipede game, and the iterated prisoner's dilemma. In general, our approach provides rational outcomes which are consistent with observed human play and might thereby resolve some of the paradoxes of game theory. 
Keywords:  noncooperative game theory, isomorphic probability spaces 
JEL:  C02 C72 
Date:  2013–04–10 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:46176&r=gth 
By:  Hassan Benchekroun; Cees Withagen 
Abstract:  We consider a nonrenewable resource game with one cartel and a set of fringe members. We show that (i) the outcomes of the closedloop and the openloop nonrenewable resource game with the fringe members as price takers (the cartel fringe game à la Salant 1976) coincide and (ii) when the number of fringe firms be comes arbitrarily large, the equilibrium outcome of the closedloop Nash game does not coincide with the equilibrium outcome of the closedloop cartelfringe game. Thus, the outcome of the cartelfringe openloop equilibrium can be supported as an outcome of a subgame perfect equilibrium. However the interpretation of the cartelfringe model, where from the outset the fringe is assumed to be pricetaker, as a limit case of an asymmetric oligopoly with the agents playing NashCournot, does not extend to the case where firms can use closedloop strategies. 
Keywords:  cartelfringe, dominant firm versus fringe, price taking, nonrenewable resources, dynamic games, openloop versus closedloop strategies 
JEL:  D43 Q30 L13 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:oxf:oxcrwp:080&r=gth 
By:  Gudmundsson, Jens (Department of Economics, Lund University) 
Abstract:  We compare different preference restrictions that ensure the existence of a stable roommate matching. Some of these restrictions are generalized to allow for indifferences as well as incomplete preference lists, in the sense that an agent may prefer remaining single to matching with some agents. We also introduce a new type of cycles and in greater detail investigate the domain of preferences that have no such cycles. In particular, we show how the absence of these cycles relates to the "symmetric utilities hypothesis" by RodriguesNeto (Journal of Economic Theory 135, 2007) when applied to roommate problems with weak preferences. 
Keywords:  Roommate problem; existence; stable matching; cycles 
JEL:  C62 C78 
Date:  2013–04–05 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2013_008&r=gth 
By:  Hitoshi Matsushima (Faculty of Economics, University of Tokyo); Tomomi Tanaka (Economic Development & Global Education, LLC); Tomohisa Toyama (Faculty of Engineering, Kogakuin University) 
Abstract:  We examine repeated prisoners' dilemma with imperfect private monitoring and random termination where the termination probability is low. We run laboratory experiments and show subjects retaliate more severely when monitoring is more accurate. This experimental result contradicts the prediction of standard game theory. Instead of assuming full rationality and pure selfinterest, we introduce naivetÃ© and social preferences, i.e., reciprocal concerns, and develop a model that is consistent with, and uniquely predicts, the observed behavior in the experiments. Our behavioral model suggests there is a tradeoff between naivetÃ© and reciprocity. When people are concerned about reciprocity, they tend to make fewer random choices. 
Date:  2013–03 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2013cf879&r=gth 
By:  Seungmoon Choi (School of Economics, University of Adelaide); Virginie Masson (School of Economics, University of Adelaide); Angus Moore; Mandar Oak (School of Economics, University of Adelaide) 
Abstract:  We develop a model of favor exchange in a network setting where the cost of performing favors is stochastic. For any given favor exchange norm, we allow for the endogenous determination of the network structure via a link deletion game. We characterize the set of stable as well as equilibrium systems and show that these sets are identical. The most efficient network topology and favor exchange convention are generically shown to be not supported as equilibrium of the link deletion game. Our model provides a useful framework for understanding the topology of favor exchange networks. While the model exhibits positive externalities, its properties differ from the "information transmission" model Ã la Jackson and Wolinsky, as evidenced by the emergence of regular networks as opposed to star networks as stable and efficient network structures. 
JEL:  D85 C78 L14 Z13 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:adl:wpaper:201304&r=gth 
By:  Yan Dolinsky 
Abstract:  We introduce a setup of model uncertainty in discrete time. In this setup we derive dual expressions for the superreplication prices of game options with upper semicontinuous payoffs. We show that the superreplication price is equal to the supremum over a special (non dominated) set of martingale measures, of the corresponding Dynkin games values. This type of results is also new for American options. 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1304.3574&r=gth 
By:  Tiziano De Angelis (University of Manchester); Giorgio Ferrari (Bielefeld University) 
Abstract:  We study a continuoustime, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a onedimensional, timehomogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investmentdisinvestment strategy. We associate to the investmentdisinvestment problem a zerosum optimal stopping game and characterize its value function through a free boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of nonlinear integral equations of Volterra type. The optimal investmentdisinvestment strategy is then shown to be a diffusion reflected at the two boundaries. 
Keywords:  reversible investment, singular stochastic control, zerosum optimal stopping games, free boundary problems, Skorokhod reflection problem 
JEL:  C02 C73 E22 D92 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:477&r=gth 
By:  Bettina Klose; Dan Kovenock 
Abstract:  We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the allpay auction with complete information and identitydependent externalities. This condition shows that the generic equilibrium of the standard allpay auction is robust to the introduction of "small" identitydependent externalities. In general, however, the presence of identitydependent externalities invalidates wellestablished qualitative results concerning the set of equilibria of the firstprice allpay auction with complete information. With identitydependent externalities equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel’s (2009) results characterizing the set of equilibrium payoffs in allpay contests, including the allpay auction as a special case, do not extend to environments with identitydependent externalities. We further compare the allpay auction with identitydependent externalities to the firstprice winnerpay auction with identitydependent externalities. We demonstrate that the equilibrium payoffs of the allpay auction and winnerpay auction cannot be ranked unambiguously in the presence of identitydependent externalities by providing examples of environments where equilibrium payoffs in the allpay auction dominate those in the winnerpay auction and vice versa. 
Keywords:  Allpay auction, identitydependent externalities, payoff nonequivalence, political conflict 
JEL:  D44 D62 D72 C72 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:118&r=gth 
By:  Ahmed Doghmiab (National Institute of Statistics and Applied Economics of Rabat, Morocco); Abderrahmane Ziad (Normandie University, Caen, Faculty of Economics and Business Administration  CREM CNRS UMR6211, France) 
Abstract:  In this paper we explore the problem of Nash implementation providing new sucient conditions called Imonotonicity and Iweak noveto power. Firstly, we show that these conditions together with unanimity are sucient for the implementation of social choice correspondences (SCCs) in Nash equilibria. Secondly, we prove that, in the domain of the private good economies with singleplateaued preferences, a solution of the problem of fair division is Nash implementable if and only if it satises Maskin monotonicity. We provide examples of SCCs satisfying or not Maskin monotonicity. 
Keywords:  Nash implementation; Private good economies; Singleplateaued preferences 
JEL:  C72 D71 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:tut:cremwp:201311&r=gth 
By:  Nobuyuki Hanaki (AixMarseille University); Nicolas Jacquemet (University of Lorraine and Paris School of Economics); Stéphane Luchini (AixMarseille University); Adam Zylbersztejn (University of Lorraine and Paris School of Economics) 
Abstract:  How much of the failures to achieve Pareto efficient outcome observed in a simple 2 2 dominance solvable game can be attributed to strategic uncertainty and how much is actually due to individual bounded rationality? We address this question by conducting a set of experiments involving two main treatments: one in which two human subjects interact, and another in which one human subject interacts with a computer program whose behavior is known. By making the behavior of the computer opponent perfectly predictable, the latter treatment eliminates strategic uncertainty. Our results suggest that observed coordination failures can be attributed equally to individual bounded rationality and strategic uncertainty. 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:uwa:wpaper:1314&r=gth 
By:  Bimonte, Giovanna 
Abstract:  It is well known that in a differential information economy the free coalition formation may imply some theoretical difficulties. It does not suffice to say that a coalition can be formed by several agents. We define a set of all possible coalitions as the set of those coalitions that can be formed and joint by any agent. There exists, in this way, a rule imposed over coalition formation. We assume that only a subset $\mathcal{S}$ of $\Sigma$ is alowed to form. In such way, we fix over the set of agents an aggregation rule for which the coalitions can be formed only if they belong to this subset. We have restricted the set of coalitions that can be joined by traders. The main result is the equivalence between two private core concept: the classical one for a differential information economy and the private core restricted. 
Keywords:  Differential information economy, restriction on coalition formation, private core. 
JEL:  D11 D51 D82 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:46283&r=gth 
By:  Hans Haller; Hans Gersbach; Hideo Konishi 
Abstract:  We consider competitive markets for multiple commodities with endogenous formation of one or twoperson households. Within each twoperson household, externalities from the partnerâ€™s commodity consumption and unpriced actions are allowed. Each individual has two types of traits: observable characteristics and unobservable taste characteristics. Each individual gets utility from his/her own private con sumption, from discrete actions such as jobchoice, from the partnerâ€™s observable characteristics such as appearance and hobbies, from some of the partnerâ€™s consumption vectors, and from the partnerâ€™s action choices. We investigate competitive market outcomes with an endoge nous household structure in which no individual and no man/womanpair can deviate profitably. We find a set of sufficient conditions under which a stable matching equilibrium exists. We further establish the first welfare theorem for this economy. 
Keywords:  endogenous household formation of households, consumption externalities, stable matching equilibrium, efficiency 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:vpi:wpaper:e0736&r=gth 