
on Game Theory 
Issue of 2012‒11‒17
twelve papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  V. Bhaskar (Department of Economics, University College, London); George J. Mailath (Department of Economics, University of Pennsylvania); Stephen Morris (Department of Economics, Princeton University) 
Abstract:  We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical noncooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents' payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player's strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one longrun player, all purifiable equilibria are Markov. 
Keywords:  Markov, bounded recall, purification 
JEL:  C72 C73 
Date:  2012–10–29 
URL:  http://d.repec.org/n?u=RePEc:pen:papers:12043&r=gth 
By:  Sylvain Béal (CRESE, Université de FrancheComté); Eric Rémila (Gate Lyon SaintEtienne, Université de Saintetienne); Philippe Solal (Gate Lyon SaintEtienne, Université de Saintetienne) 
Abstract:  We introduce new axioms for the class of all TUgames with a fixed but arbitrary player set, which require either invariance of an allocation rule or invariance of the payoff assigned by an allocation rule to a specified subset of players in two related TUgames. Comparisons with other axioms are provided. These new axioms are used to characterize the Shapley value, the equal division rule, the equal surplus division rule and the Banzhaf value. The classical axioms of efficiency, anonymity, symmetry and additivity are not used. 
Keywords:  uniform addition invariance, uniform transfer invariance, Shapley value, equal division rule, equal surplus division rule, Banzhaf value 
JEL:  C71 
Date:  2012–09 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:201201&r=gth 
By:  Marilda Sotomayor 
Abstract:  A dynamic game where agents "behave cooperatively" is postulated: At each stage, current nontrading agents can trade and the payoffs from transactions done are maintained in the subsequent stages. The game ends when no interaction is able to benefit the agents involved (case in which a core outcome is reached) or when any new interaction requires that some of the agents involved do not "behave cooperatively" (case in which the core is empty). The gains in terms of insights, obtained with this approach, allow us to identify a new condition, which is proved to be necessary and sufficient for the nonemptiness of the core. The proof of this result is elementary, in the sense that it avoids specialized mathematical tools, and only uses simple combinatorial arguments. 
Keywords:  core, simple outcome, Pareto optimal simple outcome 
JEL:  C78 D78 
Date:  2012–11–05 
URL:  http://d.repec.org/n?u=RePEc:spa:wpaper:2012wpecon30&r=gth 
By:  Sylvain Béal (CRESE, Université de Franchecomté); Amandine Ghintran (EQUIPPE, Université de Lille 3); Eric Rémila (Gate Lyon SaintEtienne, Université de Saintetienne); Philippe Solal (Gate Lyon SaintEtienne, Université de Saintetienne) 
Abstract:  We consider the problem of sharing water from a river among the group of countries located along it. The benefit of each country depends on the amount of water it consumes. An allocation of the water is efficient when it maximizes the total benefits of the countries. The problem of finding a fair welfare distribution can be modeled as a cooperative game. We introduce a new allocation rule, called the sequential equal surplus division, for sharing the total welfare resulting form the cooperation of countries along a river with bifurcations. This rule obeys the socalled Territorial Integration of all Basin States doctrine, which emphasizes compromise and fairness among countries. We provide two axiomatic characterizations of this rule. 
Keywords:  River TUgame, Sequential Equal Surplus Division, Water allocation, Standard solution, Consistency, Fairness, Amalgamation 
JEL:  C71 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:201202&r=gth 
By:  Marilda Sotomayor 
Abstract:  In the onesided Assignment game any two agents can form a partnership. If this is done, the partners undertake some joint activity, which produces a gain that is split between them. We approach this model by focusing on simple outcomes  feasible and individually rational outcomes where only unmatched agents can block. We prove that this blocking can be done in such a way that the payoffs from the trades done are not changed as players reach the core. The core is nonempty iff every simple and unstable outcome can be extended to a simple outcome by a sequence of adjustments in which, at each step, payoffs are preserved for agents already matched and increased only for those newly matching. Hence, starting from the simple outcome where everybody stands alone, we can gradually increase cooperation by making Pareto improvements (and still staying within simple outcomes), until we reach the core, or until the payoff cannot be simple anymore. That is, increase in payoffs is only available through nonoptimal cooperation of some agents. In addition, the total sum of these payoffs is the same at any core outcome. The gains in insight with this approach allows a necessary and sufficient condition for the nonemptiness of the core to be identified. Several properties of the core outcomes of economic interest are proved. 
Keywords:  matching, assignment game, core, Pareto optimal simple outcome 
JEL:  C78 D78 
Date:  2012–11–05 
URL:  http://d.repec.org/n?u=RePEc:spa:wpaper:2012wpecon27&r=gth 
By:  Antoine Mandel (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  Panthéon Sorbonne); Herbert Gintis (Santa Fe Institute  Santa Fe Institute, Central European University  CEU  Central European University) 
Abstract:  We present a mathematical model for the analysis of the bargaining games based on private prices used by Gintis to simulate the dynamics of prices in exchange economies, see [Gintis 2007]. We then characterize, in the Scarf economy, a class of dynamics for which the Walrasian equilibrium is the only stochastically stable state. Hence, we provide dynamic foundations for general equilibrium for one of the bestknown example of instability of the tâtonement process. 
Keywords:  General Equilibrium; exchange economies; bargaining games; stochastic stability. 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00748328&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  Panthéon Sorbonne, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Peter Sudhölter (University of Southern Denmark  Department of Business and Economics and COHERE) 
Abstract:  We consider TUgames with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. In such a situation, the core may be unbounded, and one has to select a bounded part of the core as a solution concept. The restricted core is obtained by imposing equality constraints in the core for sets belonging to socalled normal collections, resulting (if nonempty) in the selection of a bounded face of the core. The bounded core proves to be the union of all bounded faces (restricted cores). The paper aims at investigating in depth the relation between the bounded core and restricted cores, as well as the properties and structures of the restricted cores and normal collections. In particular, it is found that a game is convex if and only if all restricted cores corresponding to the minimal nested normal collections are nonempty. Moreover, in this case the union of these restricted cores already covers the bounded core. 
Keywords:  TUgame; restricted cooperation; distributive lattice; core; extremal rays; faces of the core. 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00748331&r=gth 
By:  Marilda Sotomayor 
Abstract:  We consider two twosided matching markets, where every agent has an amount of units of a divisible good to be distributed among the partnerships he forms and exchanged for money. Both markets have the same sets of feasible allocations but operate under distinct rules. However they are indistinguishable under their representation in the characteristic function form. The adequate and proposed mathematical model provides the foundation to characterize the cooperative equilibrium concept in each market. Setwisestability is then shown not to be the general definition of stability. The connection between the cooperative structures of these markets and between the cooperative and competitive structures of each market is established, by focusing on the algebraic structure of the core, the set of cooperative equilibrium allocations and the set of competitive equilibrium allocations. The results obtained and the methodology used in their proofs provide new and useful insights to the theory of twosided matching markets. 
Keywords:  stable allocations, core, competitive equilibrium allocations, feasible deviation 
JEL:  C78 D78 
Date:  2012–11–05 
URL:  http://d.repec.org/n?u=RePEc:spa:wpaper:2012wpecon29&r=gth 
By:  Ismail Saglam (TOBB University of Economics and Technology, Department of Economics) 
Abstract:  This paper introduces a class of endogenously proportional bargaining solutions. These solutions are independent of the class of Directional solutions, which Chun and Thomson (1990a) proposed to generalize (exogenously) proportional solutions of Kalai (1977). Endogenously proportional solutions relative to individual i are characterized by weak Pareto optimality and continuity together with two new axioms that depend on the pairwise total payoff asymmetry of the bargaining problem with respect to each pair involving individual i. Each of these solutions satisfies the basic symmetry axiom and also a stronger axiom called total payoff symmetry. 
Keywords:  Cooperative bargaining; proportional solutions; symmetry 
JEL:  C71 C78 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:koc:wpaper:1232&r=gth 
By:  Marilda Sotomayor 
Abstract:  We prove two Folk Theorems which, together with the NonManipulability Theorem (Demange (1982) and Leonard (1983)), have stimulated the development of the theory on incentives for the onetoone twosided matching models with money as a continuous variable. 
Keywords:  matching, Stable payoff, competitive equilibrium payoff, optimal stable payoff 
JEL:  C78 D78 
Date:  2012–11–05 
URL:  http://d.repec.org/n?u=RePEc:spa:wpaper:2012wpecon28&r=gth 
By:  He, Yinghua; Yan, Jianye 
Abstract:  Competitive Equilibrium from Equal Incomes for TwoSided Matching 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 di¤erent prices depending on how schools rank them. It always produces fair (justifiedenvyfree) and ex ante e¢ cient random assignments and stable deterministic assignments if both students and schools are truthtelling. We show that each student's incentive to misreport vanishes when the market becomes large, given all others are truthful. The mechanism is particularly relevant to school choice as schools' priority orderings over students are usually known and can be considered as their ordinal preferences. More importantly, in settings like school choice where agents have similar ordinal preferences, the mechanismis explicit use of cardinal preferences may significantly improve eficiency. We also discuss its application in school choice with groupspecific quotas and in onesided matching. 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:26415&r=gth 
By:  Raphaële Préget; Phu NguyenVan; Marc Willinger 
Abstract:  We show that the preference to act as a leader rather than as a follower is related to subjects’ behavioral type. We rely on the methodology proposed by Fischbacher et al. (2001) and Fischbacher and Gächter (2010) in order to identify subjects’ behavioral types. We then link the likelihood to act as a leader in a repeated public goods game to the elicited behavioral types. The leader in a group is defined as the subject who voluntarily decides in the first place about his contribution. The leader’s contribution is then reported publicly to the remaining group members who are requested to take their contribution decisions simultaneously. Our main findings are that leaders emerge in almost all rounds and that conditional cooperators are more likely to act as leaders compared to free riders. We also find that voluntary leaders, irrespective of their behavioral type, contribute more than the followers. However leadership does not prevent the decay that is commonly observed in linear public goods experiments. 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:lam:wpaper:1234&r=gth 