
on Game Theory 
Issue of 2013‒07‒15
nineteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Oikonomou, V.K.; Jost, J 
Abstract:  We define and study periodic strategies in two player finite strategic form games. This concept can arise from some epistemic analysis of the rationalizability concept of Bernheim and Pearce. We analyze in detail the pure strategies and mixed strategies cases. In the pure strategies case, we prove that every two player finite action game has at least one periodic strategy, making the periodic strategies an inherent characteristic of these games. Applying the algorithm of periodic strategies in the case where mixed strategies are used, we find some very interesting outcomes with useful quantitative features for some classes of games. Particularly interesting are the implications of the algorithm to collective action games, for which we were able to establish the result that the collective action strategy can be incorporated in a purely noncooperative context. Moreover, we address the periodicity issue for the case the players have a continuum set of strategies available. We also discuss whether periodic strategies can imply any sort of cooperativity. In addition, we put the periodic strategies in an epistemic framework. 
Keywords:  Game Theory;Rationalizability;Solution Concepts, Periodicity;Epistemic Game Theory 
JEL:  C0 C02 C70 C72 
Date:  2013–07–08 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48117&r=gth 
By:  Mario Bravo (Instituto de Sistemas Complejos de Ingenieria (ISCI), Universidad de Chile); Mathieu Faure (AixMarseille University (AixMarseille School of Economics), CNRS & EHESS) 
Abstract:  Consider a 2player normalform game repeated over time. We introduce an adaptive learning procedure, where the players only observe their own realized payoff at each stage. We assume that agents do not know their own payoff function, and have no information on the other player. Furthermore, we assume that they have restrictions on their own action set such that, at each stage, their choice is limited to a subset of their action set. We prove that the empirical distributions of play converge to the set of Nash equilibria for zerosum and potential games, and games where one player has two actions. 
Keywords:  Reinforcement learning, fictitious play, Markovian procedures. 
Date:  2013–07–01 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:1335&r=gth 
By:  Sébastien Courtin; Bertrand Tchantcho (THEMA, University of CergyPontoise, France.; University of Yaounde I, Advanced Teachers’ Training College,) 
Abstract:  The desirability relation was introduced by Isbell (1958) to qualitatively compare the a priori influence of voters in a simple game. In this paper, we extend this desirability relation to simple games with coalition structure. In these games, players organize themselves into a priori disjoint coalitions. It appears that the desirability relation defined in this paper is a complete preorder in the class of swaprobust games. We also compare our desirability relation with the preorders induced by the generalizations to games with coalition structure of the ShapleyShubik and BanzahfColeman power indices (Owen, 1977, 1981). It happens that in general they are different even if one considers the subclass of weighed voting games. However, if structural coalitions have equal size then both OwenBanzhaf and the desirability preordering coincide. 
Keywords:  Voting games; Coalition structure; Power indices; Desirability relation 
JEL:  C71 D72 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201330&r=gth 
By:  Linda Sass (Center for Mathematical Economics, Bielefeld University) 
Abstract:  Riedel and Sass (2013) propose a framework for normal form games where players can use imprecise probabilistic devices. We extend this strategic use of objective ambiguity to extensive form games. We show that with rectangularity of Ellsberg strategies we have dynamic consistency in the sense of Kuhn (1953): rectangular Ellsberg strategies are equivalent to Ellsberg behavior strategies. We provide an example for our result and define Ellsberg equilibrium in such extensive form Ellsberg games. 
Keywords:  Knightian Uncertainty in Games, Objective Ambiguity, Strategic Ambiguity, Extensive Form Ellsberg Games, Kuhn's Theorem, Rectangularity 
JEL:  C72 C73 D81 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:478&r=gth 
By:  Jason Shachat (Wang Yanan Institute for Studies in Economics (WISE) and the MOE Key Laboratory in Econometrics, Xiamen University, Xiamen, Fujian Province, 361005, China); J. Todd Swarthout (Department of Economics, Georgia State University, Atlanta, GA, 30303, USA) 
Abstract:  We conduct an experiment in which we auction the scarce rights to play the Proposer and Responder positions in subsequent ultimatum games. As a control treatment, we randomly allocate these rights and then charge exogenous participation fees according to the auction price sequences observed in the auction treatment. With endogenous selection into ultimatum games via auctions, we find that play converges to a sessionspecific Nash equilibrium and auction prices emerge which support this equilibrium by the principle of forward induction. With random assignment and exogenous participation fees, we find play also converges to a sessionspecific Nash equilibrium as predicted by the principle of loss avoidance. The Nash equilibrium observed within a session results in low ultimatum game offers, but the subgame perfect Nash equilibrium is never observed. 
Keywords:  Ultimatum Bargaining, Auction, Forward Induction 
JEL:  C92 C78 D44 
Date:  2013–03–28 
URL:  http://d.repec.org/n?u=RePEc:fee:wpaper:1301&r=gth 
By:  Ulrich Faigle (Universität zu Köln  Mathematisches Institut); Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  The Shapley value is defined as the average marginal contribution of a player, taken over all possible ways to form the grand coalition N when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general model of coalition formation where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is weaker than the one in the original paper but allows a much more transparent correctness proof. Moreover, the logical independence of the axioms is proved. 
Keywords:  Coalitional game; coalition formation process; Shapley value 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00841259&r=gth 
By:  George J. Mailath (Department of Economics, University of Pennsylvania); Larry Samuelson (Department of Economics, Yale University) 
Abstract:  This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in repeated games of incomplete information. 
Keywords:  commitment, incomplete information, reputation bound, reputation effects, longrun relationships, reputations 
JEL:  C70 C73 
Date:  2013–06–27 
URL:  http://d.repec.org/n?u=RePEc:pen:papers:13034&r=gth 
By:  Billand, P.; Bravard, C.; Kamphorst, J.; Sarangi, S. 
Abstract:  Social networks, be it on the internet or in real life, facilitate information flows. We model this by giving agents incentives to link with others and receive information through those links. We consider networks where agents have an incentive to confirm the information they receive from others. Our paper analyzes the social networks that are formed. We first study the existence of Nash equilibria and then characterize the set of strict Nash networks. Next, we characterize the set of strictly efficient networks and discuss the relationship between strictly efficient networks and strict Nash networks. Finally, we check the robustness of our results by allowing for heterogeneity among agents, possibility of bilateral deviations of agents, and decay in network. 
Keywords:  R&D COLLABORATION;NETWORK FORMATION;MULTIMARKET OLIGOPOLIES 
JEL:  C72 D85 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:gbl:wpaper:201306&r=gth 
By:  Giuseppe De Marco (Università di Napoli Parthenope and CSEF); Maria Romaniello (Seconda Università di Napoli) 
Abstract:  In this paper we consider a model of games of incomplete information under ambiguity in which players are endowed with variational preferences. We provide an existence result for the corresponding mixed equilibrium notion. Then we study the limit behavior of equilibria under perturbations on the indices of ambiguity aversion. 
Keywords:  Incomplete information games, multiple priors, variational preferences, equilibria 
Date:  2013–07–09 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:336&r=gth 
By:  Steven, Brams; Marc, Kilgour 
Abstract:  Gale and Shapley (1962) proposed the deferredacceptance algorithm for matching (i) college applicants and colleges and (ii) men and women. In the case of the latter, it produces either one or two stable matches whereby no man and woman would prefer to be matched with each other rather than with their present partners. But stable matches can give one or both players in a pair their worst match, whereas the minimax algorithm that we propose, which finds all assignments that minimize the maximum rank of players in matches, avoids such assignments. Although minimax matches may not be stable, at least one is always Paretooptimal: No other matching is at least as good for all the players and better for one or more. If there are multiple minimax matches, we propose criteria for choosing the most desirable among them and also discuss the settings in which minimax matches seem more compelling than deferredacceptance matches when they differ. Finally, we calculate the probability that minimax matches differ from deferredacceptance matches in a simple case. 
Keywords:  Deferredacceptance algorithm; minimax algorithm; matchings; stability 
JEL:  C71 C78 D7 D71 D78 
Date:  2013–07–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48113&r=gth 
By:  Newton, Jonathan; Sawa, Ryoji 
Abstract:  This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to oneshot deviation. 
Keywords:  college admissions; marriage; matching; stochastic stability; learning 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:syd:wpaper:2123/9223&r=gth 
By:  Riedl A.M.; Dariel A. (GSBE) 
Abstract:  We elicit reciprocal preferences in a firmworker giftexchange setting and relate them to actual behavior in a repeated giftexchange game. We find that only a small minority of 10 percent of workers is materially selfish whereas 90 percent exhibit reciprocal preferences. However, the intensity of reciprocal preferences is weak in the sense that firms maximize profits by not relying on giftexchange but by offering the lowest possible wage. Workers behavior in the repeated giftexchange game is predicted by their elicited preferences, but the correlation between preferences and behavior is imperfect. Together with profit maximizing behavior of firms these observations can explain the observed unraveling of giftexchange over time in our experiment and some recent field experiments. 
Keywords:  Noncooperative Games; Design of Experiments: Laboratory, Group Behavior; LaborManagement Relations, Trade Unions, and Collective Bargaining: Other; 
JEL:  C72 C92 J59 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:umagsb:2013034&r=gth 
By:  Joachim Rosenmüller (Center for Mathematical Economics, Bielefeld University) 
Abstract:  We consider (cooperative) linear production games with a continuum of players. The coalitional function is generated by r + 1 “production factors” that is, non atomic measures defined on an interval. r of these are orthogonal probabilities which, economically, can be considered as “cornered” production factors. The r+1th measure involved has positive mass “across the carriers” of the orthogonal probabilities. That is, there is a “non–cornered” (or “central”) production factor available throughout the market. We consider convex vNM–Stable Sets of this game. Depending on the size of the central measure, we observe cases in which a vNM–Stable Set is uniquely defined to be either the core or the convex hull of the core plus a unique additional imputation. We observe other situations in which a variety of vNM–Stable Sets exists. Within this first part we will present the coalitions that are necessary and sufficient for dominance relations between imputations. In the context of the “purely orthogonal” production game this question is answered in a rather straightforward way by the “Inheritance Theorem” established in [3]. However, once orthogonality is abandoned one has to establish prerequisites about epsilon–relevant coalitions. Thus, this first part centers around the formulation of a generalized “Inheritance Theorem”. As a consequence, based on the Inheritance Theorem, we provide conditions for the core to be a vNM–Stable Set whenever the central commodity is available in abundance. 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:483&r=gth 
By:  Billand, P.; Bravard, C.; Chakrabarti, S.; Sarangi, S. 
Abstract:  In this note, we extend the Goyal and Joshi's model of network of collaboration in oligopoly to multimarket situations. We examine the incentive of firms to form links and the architectures of the resulting equilibrium networks of this setting. We also present some results on efficient networks. 
Keywords:  R&D COLLABORATION;NETWORK FORMATION;MULTIMARKET OLIGOPOLIES 
JEL:  C70 L13 L20 D85 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:gbl:wpaper:201305&r=gth 
By:  Kohler, Stefan 
Abstract:  This note presents a solution to Rubinstein (1982)'s openended, alternatingoffer bargaining problem for two equally patient bargainers that exhibit similar degrees of inequality aversion. Inequalityaverse bargainers may perceive envy if being worse off and guilt if being better off, but they still reach agreement in the first period under complete information. If the perceived guilt is strong, then the inequalityaverse bargainers split the bargaining surplus equally regardless of their degree of envy. If guilt is weak, then the agreed split is tilted away from the Rubinstein division towards a more unequal split. Envy and weak guilt have opposite effects on the bargaining outcome, and envy has a greater marginal impact than weak guilt. Similarly inequalityaverse bargainers agree on the Rubinstein division if the strength of envy equals the discounted strength of guilt. As both bargainers sensation of inequality aversion diminishes, the bargaining outcome converges to the Rubinstein division. 
Keywords:  alternating offers; bargaining; bargaining power; behavioral economics; envy; equity; fairness; guilt; negotiation; social preferences 
JEL:  C78 D3 D63 
Date:  2013–07–06 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:40764&r=gth 
By:  Fabio Sferra (Fondazione Eni Enrico Mattei, EuroMediterranean Center on Climate Change, Italy); Massimo Tavoni (Fondazione Eni Enrico Mattei, EuroMediterranean Center on Climate Change, Italy) 
Abstract:  Our purpose is to analyse the effectiveness and efficiency of a Partial Climate Agreement with open entry under a noncooperative NashEquilibrium framework. We evaluate a partial agreement policy in which nonsignatory countries can decide to join or to leave a coalition of the willing at any point in time. By means of a simple analytical model and of a numerical integrated assessment model, we assess different coalition structures, and different minimum admission requirements. Our results indicate that a Partial Climate Agreement with open entry can be effective, achieving climate stabilization between 2C and 3C depending on the composition of the coalition of the willing. The policy turns out to be also rather efficient, with only minor losses with respect to a full cooperation agreement. Finally, we quantify the optimal admission requirement in about 4050% of cumulative abatement. 
Keywords:  International Environmental Agreements, NonBinding Targets, Voluntary Climate Change Actions, Optimal Mitigation Strategies, Fair Burden Sharing in Climate Negotiations, Carbon Leakage 
JEL:  C72 F18 Q54 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2013.60&r=gth 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Achim Wambach (Dept. of Economics, University of Cologne) 
Abstract:  We consider the design of an optimal auction in which the seller can determine the allocation and the disclosure rule of the mechanism. Thus, in contrast to the standard analysis of a optimal auctions, the seller can explicitly design the disclosure of the information received by each bidder as his private information. We show that the optimal disclosure rule is a sequential disclosure rule, implemented in an ascending price auction. In the optimal disclosure mechanism, each losing bidder learns his true valuation, but the winning bidder only learns that his valuation is sufficiently high to win the auction. We show that in the optimal auction, the posterior incentive and participation constraints of all the bidders are satisfied. In the special case in which the bidders have no private information initially, the seller can extract the entire surplus. 
Keywords:  Independent private value auction, Sequential disclosure, Ascending auctions, Information structure, Interim equilibrium, Posterior equilibrium 
JEL:  C72 D44 D82 D83 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1900&r=gth 
By:  Thomas Michielsen (Tilburg University) 
Abstract:  I analyze optimal natural resource use in an intergenerational model with the risk of a catastrophe. Each generation maximizes a weighted sum of discounted utility (positive) and the probability that a catastrophe will occur at any point in the future (negative). The model generates time inconsistency as generations disagree on the relative weights on utility and catastrophe prevention. As a consequence, future generations emit too much from the current generation’s perspective and a dynamic game ensues. I consider a sequence of models. When the environmental problem is related to a scarce exhaustible resource, early generations have an inincentive to reduce emissions in Markov equilibrium in order to enhance the ecosystem’s resilience to future emissions. When the pollutant is expected to become obsolete in the near future, early generations may however in crease their emissions if this reduces future emissions. When polluting inputs are abundant and expected to remain essential, the catastrophe becomes a selffulfilling prophecy and the degree of concern for catastrophe prevention has limited or even no effect on equilibrium behaviour. 
Keywords:  Catastrophic Events, Decision Theory, Uncertainty, Time Consistency 
JEL:  C73 D83 Q54 
Date:  2013–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2013.55&r=gth 
By:  Nizar Allouch (, Queen Mary, University of London, School of Economics and Finance, UK) 
Abstract:  This paper investigates the private provision of public goods in segregated societies. While most research agrees that segregation undermines public provision, the findings are mixed for private provision: social interactions, being strong within groups and limited across groups, may either increase or impede voluntary contributions. Moreover, although efficiency concerns generally provide a rationale for government intervention, surprisingly, little light is shed in the literature on the potential effectiveness of such intervention in a segregated society. This paper first develops an index based on social interactions, which, roughly speaking, measures the welfare impact of income redistribution in an arbitrary society. It then shows that the proposed index vanishes when applied to large segregated societies, which suggests an “asymptotic neutrality” of redistributive policies. 
Keywords:  Public Goods, Segregated Society, Private Provision, Networks, Bonacich Transfer Index 
JEL:  C72 D31 H41 
Date:  2013–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2013.52&r=gth 