
on Game Theory 
Issue of 2013‒05‒22
twelve papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Herve Moulin; Indrajit Ray; Sonali Sen Gupta 
Abstract:  We consider coarse correlated equilibria  CCE  (Moulin and Vial 1978) for the wellanalyzed abatement game (Barrett 1994) and prove that CCE 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: it is achieved by a CCE involving only two pure strategy profiles, and the efficiency gain is small. 
Keywords:  Coarse correlated equilibrium, Abatement game 
JEL:  C72 Q52 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:bir:birmec:1311&r=gth 
By:  Olivier Compte (Paris School of Economics); Andrew Postlewaite (Department of Economics, University of Pennsylvania) 
Abstract:  The repeated game literature studies long run/repeated interactions, aiming to understand how repetition may foster cooperation. Conditioning future behavior on past play is crucial in this endeavor. For most situations of interest a given player does not directly observe the actions chosen by other players and must rely on noisy signals he receives about those actions. This is typically incorporated into models by defining a monitoring structure, that is, a collection of probability distributions over the signals each player receives (one distribution for each action profile players may play). Although this is simply meant to capture the fact that players don.t directly observe the actions chosen by others, constructed equilibria often depend on players precisely knowing the distributions, somewhat unrealistic in most problems of interest. This paper aims to show the fragility of belief free equilibrium constructions when one adds shocks to the monitoring structure in repeated games. 
Keywords:  Repeated games, folk theorem, belief free, robustness 
JEL:  C72 C73 
Date:  2013–05–10 
URL:  http://d.repec.org/n?u=RePEc:pen:papers:13020&r=gth 
By:  Raul V. Fabella (University of the Philippines School of Economics); Vigile Marie B. Fabella (Universitët Konstanz, Germany) 
Abstract:  We propose an equilibrium concept, the Robust Nash equilibrium (RNE), that combines the bestreply rationality and the "first mover invariance" condition. The singlestage 2x2 symmetric information game G is transformed into sequential twostage games with two subtrees: STA has the row player starting and STB has the column player starting. A profile in G is robust if it is the strict SPNE of the two branches; it is ephemeral if it is not the SPNE of any branch. We show that every strict dominant strategy equilibrium of G is robust but not every strict Nash equilibrium of G is. We show further that every robust profile of G is always a strict Nash equilibrium of G. A Robust Nash equilibrium (RNE) of G is any robust profile of G. The RNE of G is unique. We show in particular that the payoff dominant strict Nash equilibrium of a coordination game G is RNE while the strictly payoffdominated Nash equilibrium of G is ephemeral. The original HarsanyiSelten preference for payoff dominance over risk dominance is supported by robustness without invoking collective rationality. 
Keywords:  Nash Equilibrium 
JEL:  C02 C72 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:phs:dpaper:201216&r=gth 
By:  Indrajit Ray; Susan Snyder 
Abstract:  We provide necessary and sufficient conditions for observed outcomes in extensive game forms, in which preferences are unobserved, to be rationalized first, weakly, as a Nash equilibrium and then, fully, as the unique subgameperfect equilibrium. Thus, one could use these conditions to find that play is (a) consistent with subgameperfect equilibrium, or (b) not consistent with subgameperfect behavior but is consistent with Nash equilibrium, or (c) consistent with neither. 
Keywords:  Revealed Preference, Consistency, Subgame Perfect Equilibrium 
JEL:  C72 C92 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:bir:birmec:0414r&r=gth 
By:  Paula Jaramillo; Çagatay Kayi; Flip Klijn 
Abstract:  This paper studies manytoone matching markets where each student is assigned to a hospital. Each hospital has possibly multiple positions and responsive preferences. We study the game induced by the studentoptimal stable matching mechanism. We assume that students play their weakly dominant strategy of truthtelling. Roth and Sotomayor (1990) showed that there can be unstable equilibrium outcomes. We prove that any stable matching can be obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the socalled ‘rural hospital theorem' cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to onetoone matching markets, (a) filled positions depend on the particular equilibrium that is reached and (b) welfare levels are not bounded by the student and hospitaloptimal stable matchings (with respect to the true preferences). 
Date:  2013–04–10 
URL:  http://d.repec.org/n?u=RePEc:col:000089:010737&r=gth 
By:  Subhasish M. Chowdhury (University of East Anglia, Norwich); Dongryul Lee (Department of Economics, Sungshin University, Seoul); Roman M. Sheremeta (Chapman University) 
Abstract:  We analyze a group contest in which n groups compete to win a groupspecific public good prize. Group sizes can be different and any player may value the prize differently within and across groups. Players exert costly efforts simultaneously and independently. Only the highest effort (the bestshot) within each group represents the group effort that determines the winning group. We fully characterize the set of equilibria and show that in any equilibrium at most one player in each group exerts strictly positive effort. There always exists an equilibrium in which only the highest value player in each active group exerts strictly positive effort. However, perverse equilibria may exist in which the highest value players completely freeride on others by exerting no effort. We provide conditions under which the set of equilibria can be restricted and discuss contest design implications. 
Keywords:  bestshot technology; group contest; groupspecific public goods; freeriding 
JEL:  C72 D70 D72 H41 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:chu:wpaper:1312&r=gth 
By:  Yinghua He; Antonio Miralles; Jianye Yan 
Abstract:  Using the assignment of students to schools as our leading example, we study manytoone twosided matching markets without transfers. Students are endowed with cardinal preferences and schools with ordinal ones, while preferences of both sides need not be strict. Using the idea of a competitive equilibrium from equal incomes (CEEI, Hylland and Zeckhauser (1979)), we propose a new mechanism, the Generalized CEEI, in which students face different prices depending on how schools rank them. It always produces fair (justifiedenvyfree) and ex ante efficient random assignments and stable deterministic ones with respect to stated preferences. Moreover, if a group of students are top ranked by all schools, the GCEEI random assignment is ex ante weakly efficient with respect to studentsâ€™ welfare. We show that each studentâ€™s incentive to misreport vanishes when the market becomes large, given all others are truthful. The mechanism is particularly relevant to school choice since schoolsâ€™ priority orderings can be considered as their ordinal preferences. More importantly, in settings where agents have similar ordinal preferences, the mechanismâ€™s explicit use of cardinal preferences may significantly improve efficiency. We also discuss its application in school choice with affirmative action such as groupspecific quotas and in onesided matching. 
Keywords:  twosided matching, weak preferences, school choice, efficiency, fairness, stability, incentive compatibility, competitive equilibrium from equal incomes 
JEL:  C78 D82 I29 
Date:  2012–12 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:692&r=gth 
By:  Hannes Rusch 
Abstract:  The Prisoner’s Dilemma (PD) is widely used to model social interaction between un related individuals in the study of the evolution of cooperative behaviour in humans and other species. Many effective mechanisms and promotive scenarios have been studied which allow for small founding groups of cooperative individuals to prevail even when all social interaction is characterised as a PD. Here, a brief critical discusion of the role of the PD as the most prominent tool in cooperation research is presented, followed by two new objections to such an exclusive focus on PDbased models of social interaction. It is highlighted that only 2 of the 726 combinatorially possible strategically unique ordinal 2x2 games have the detrimental characteristics of a PD and that the frequency of PDtype games in a space of games with random payoffs does not exceed about 3.5%. Although these purely mathematical considerations do not compellingly imply that the relevance of PDs is overestimated, it is proposed that, in the absence of convergent empirical information about the ancestral human social niche, this finding can be interpreted in favour of a so far rather neglected answer to the question of how the founding groups of human cooperation themselves came to cooperate: Behavioural and/or psychological mechanisms which evolved for other, possibly more frequent, social interaction situations might have been applied to PD type dilemmas only later. Human cooperative behaviour might thus partly have begun as a cooptation. 
Keywords:  cooperation, prisoner’s dilemma, cooptation, social niche, human evolution 
JEL:  C73 D74 D79 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:mar:magkse:201327&r=gth 
By:  Desirée Desierto (School of Economics, University of the Philippines Diliman) 
Abstract:  Using spatial Poisson processes, we reinterpret the Imitation Dynamics and show how the spatial clustering of players affects both the selection of strategies and the speed by which they replicate. We find that the more clustered are the players, (a) the faster the evolution of strategies and (b) if some players have inherent preferences for a strategy, the greater the probability of mutation into, and selection of, that preferred strategy. 
JEL:  C78 
Date:  2012–02 
URL:  http://d.repec.org/n?u=RePEc:phs:dpaper:201204&r=gth 
By:  Luca Lambertini (Department of Economics, University of Bologna and Rimini Centre for Economic Analysis, Italy) 
Abstract:  The model proposed in this paper investigates a differential Cournot oligopoly game with nonrenewable resource exploitation, in which each firm may exploit either its own private pool or a common pool jointly with the rivals. Firms use a deterministic technology to invest in exploration activities. There emerges that (i) the individual exploration effort is higher when each firms has exclusive rights on a pool of its own, and (ii) depending on whether each firm has access to its own pool or all firms exploit a common one, the aggregate exploration effort is either increasing or constant in the number of firms. 
Keywords:  di¤erential games, natural resources, oligopoly 
JEL:  C73 L13 Q30 
Date:  2013–05 
URL:  http://d.repec.org/n?u=RePEc:rim:rimwps:25_13&r=gth 
By:  M. D. Farjam; M. Faillo; W.F.G. Haselager; I.G. SprinkhuizenKuyper 
Abstract:  In social dilemmas punishment costs resources, not just from the one who is punished but often also from the punisher and society. Reciprocity on the other side is known to lead to cooperation without the costs of punishment. The question at hand is whether punishment besides its costs brings advantages and how its negative sideeffects can be reduced to a minimum in an environment populated by reciprocal agents. Various punishment mechanisms have been studied in the economic literature such as unrestricted punishment, legitimate punishment, cooperative punishment, and the hired gun mechanism. All these mechanisms are implemented in a simulation where agents can share resources and may decide to punish other agents when they do not share. Through evolutionary learning agents adapt their sharing/punishing policy. Despite the costs of punishment, legitimate punishment compared to nopunishment increased performance when the availability of resources was low. When the availability was high, performance was better in nopunishment conditions with indirect reciprocity. Furthermore the hired gun mechanism worked only as good as other punishment mechanisms when the availability of resources was high. Legitimate punishment leads to a higher performance than unrestricted punishment. Summarized, this paper shows that a wellchosen punishment mechanism can play a facilitating role for cooperation even if the cooperating system already adopted reciprocity. 
Keywords:  Public Goods Games, Punishment, Cooperation, Reciprocity, Evolution of Cooperation 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:trn:utwpce:1302&r=gth 
By:  Fulvio Fontini (Department of Economics and Management  University of Padua); Katrin Millock (Centre d'Economie de la Sorbonne  Paris School of Economics); Michele Moretto (Department of Economics and Management  University of Padua) 
Abstract:  In many cases consumers cannot observe firms' investment in quality or safety, but have only beliefs on the average quality of the industry. In addition, the outcome of the collective investment game of the firms may be stochastic since firms cannot control perfectly the technology or external factors that may affect production. In such situations, when only consumers' subjective perceptions of the industry level of quality matters, the regulator may make information available to firms or subsidize their information acquisition. Under what conditions is it desirable to make information available? We show how firms' overall level of investment in quality depends upon the parameters of the quality accumulation process, the cost of investment and the number of firms in the industry. We also show the potentially negative effects on the total level of quality from providing information on consumers' actual valuation. 
Keywords:  Collective reputation, option value, quality. 
JEL:  C73 D92 L15 Q52 
Date:  2013–05 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:13044&r=gth 