
on Game Theory 
Issue of 2014‒06‒02
fourteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Eliaz, Kfir; Spiegler, Rani 
Abstract:  What is common to the following situations: incentivizing collective action in the presence of social preferences, monopoly pricing when consumers are loss averse, arms races when players are privately informed of their armament costs? We present a simple formalism, called Xgames, which unifies these situations as well as others, and use it to unify and extend the separate analyses that they received in the literature. 
Keywords:  Contagion; Coordination; Externalities; Strategic complementarities 
JEL:  C72 
Date:  2014–02 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9814&r=gth 
By:  Luís Carvalho 
Abstract:  This paper oers a constructive proof of the Nash Bargaining solution. We start by proving that Nashs solution is representable based on its continuity. This property along with the linearity of the choice function will then allow us to identify the function representing Nashs bargaining choice. Finally, supported on the result for two players, we will generalize it to nplayers. 
Keywords:  Nash Bargaining; Constructive Proof 
JEL:  C73 
Date:  2014–05–22 
URL:  http://d.repec.org/n?u=RePEc:isc:iscwp2:bruwp1401&r=gth 
By:  Krumer, Alex; Megidish, Reut; Sela, Aner 
Abstract:  We study roundrobin tournaments with three players whose values of winning are common knowledge. In every stage a pairwise match is modelled as an allpay auction. The player who wins in two matches wins the tournament. We characterize the subgame perfect equilibrium for symmetric (all players have the same value) and asymmetric players (each one is either weak (low value) or strong (high value)) and prove that if the asymmetry between the players' values are relatively weak, each player maximizes his expected payoff if he competes in the first and the last stages of the tournament. Moreover, even when the asymmetry between the players' values are relatively strong, the strong players maximize their expected payoffs if they compete in the first and the last stages. We show that a contest designer who wishes to maximize the length of the tournament such that the winner of the tournament will be decided in the last stage should allocate the stronger players in the last stage. But if he wishes to maximize the players' expected total effort he should not allocate them in the last stage of the tournament. 
Keywords:  Allpay auctions; Roundrobin tournaments 
JEL:  D44 D72 D82 
Date:  2014–03 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9873&r=gth 
By:  Giuseppe De Marco (Università di Napoli Parthenope and CSEF); Maria Romaniello (Università di Napoli Federico II) 
Abstract:  In previous papers we studied a game model in which players' uncertainty is expressed entirely in the space of probabilities (lotteries) over consequences, it depends on the entire strategy profile chosen by the agents and it is described by the so called ambiguous beliefs correspondences. In this paper, we extend the previous results by embodying variational preferences in the model. We give a general existence result that we apply to a particular example in which beliefs correspondences depend on the equilibria of specific subgames. Then, we study the limit behavior of equilibria under perturbations on the index of ambiguity aversion. 
Date:  2014–05–20 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:363&r=gth 
By:  Minchuk, Yizhaq; Sela, Aner 
Abstract:  We study allpay auctions with multiple prizes. The players have the same value for all the certain prizes except for one uncertain prize for which each player has a private value. We characterize the equilibrium strategy and show that if the number of prizes is smaller than the number of players, independent of the ranking of the uncertain prize, a player's probability to win as well as his expected utility increases in his value for this prize. We demonstrate that a stochastic dominance relation between two distribution functions of the players' private values may increase but also even decrease the players' exante expected utility as well the players' expected total effort. Also, increasing the number of prizes may decrease the players' exante expected utility. Thus, we may conclude that a larger number of prizes does not necessarily benefit the players in a contest. 
Keywords:  Allpay auctions; contests; uncertain prizes 
JEL:  D44 D82 J31 J41 
Date:  2014–03 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9908&r=gth 
By:  Kojima, Fuhito; Tamura, Akihisa; Yokoo, Makoto 
Abstract:  In this paper, we consider twosided, manytoone matching problems where agents in one side of the market (hospitals) impose some distributional constraints (e.g., a minimum quota for each hospital). We show that when the preference of the hospitals is represented as an Mnaturalconcave function, the following desirable properties hold: (i) the time complexity of the generalized GS mechanism is O(X^3), where X is the number of possible contracts, (ii) the generalized Gale & Shapley (GS) mechanism is strategyproof, (iii) the obtained matching is stable, and (iv) the obtained matching is optimal for the agents in the other side (doctors) within all stable matchings. Furthermore, we clarify sufficient conditions where the preference becomes an Mnaturalconcave function. These sufficient conditions are general enough so that they can cover most of existing works on strategyproof mechanisms that can handle distributional constraints in manytoone matching problems. These conditions provide a recipe for nonexperts in matching theory or discrete convex analysis to develop desirable mechanisms in such settings. 
Keywords:  twosided matching, manytoone matching, strategyproof mechanism, deferred acceptance, distributional constraints, discrete convex analysis 
JEL:  C71 C78 D61 
Date:  2014–04–30 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:56189&r=gth 
By:  F. Delbono; L. Lambertini 
Abstract:  A well established belief both in the gametheoretic IO and in policy debates is that market concentration facilitates collusion. We show that this piece of conventional wisdom relies upon the assumption of profitseeking behaviour, for it may be reversed when firms pursue other plausible goals. To illustrate our intuition, we investigate the incentives to tacit collusion in an industry formed by LaborManaged (LM) enterprises. We characterize the perfect equilibrium of a supergame in which LM firms play an infinitely repeated Cournot game. We show that the critical threshold of the discount factor above which collusion is stable (i) is lower in the LM industry than in the capitalistic one; (ii) monotonically decreases with the number of firms. 
JEL:  L1 L3 C7 
Date:  2014–05 
URL:  http://d.repec.org/n?u=RePEc:bol:bodewp:wp948&r=gth 
By:  Blanchet, Adrien; Carlier, Guillaume 
Abstract:  The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of N player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article we emphasize the role of optimal transport theory in: 1) the passage from Nash to CournotNash equilibria as the number of players tends to infinity, 2) the analysis of CournotNash equilibria. 
Keywords:  Nash equilibria, games with a continuum of players, CournotNash equilibria, MongeKantorovich optimal transportation problem 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:28213&r=gth 
By:  Bonatti, Alessandro; Rantakari, Heikki 
Abstract:  A team must select among competing projects that differ in their payoff consequences for its members. Each agent chooses a project and exerts costly effort affecting its random completion time. When one or more projects are complete, agents bargain over which one to implement. A consensus requirement can (but need not) induce the efficient balance between compromise in project selection and equilibrium effort. Imposing deadlines for presenting counteroffers is beneficial, while delegating decisionmaking to an impartial third party leads agents to select extreme projects. Finally, hiring agents with opposed interests can foster both effort and compromise in project selection. 
Keywords:  bargaining; compromise; conflict; consensus; deadlines; freeriding 
JEL:  C72 D71 D83 
Date:  2014–03 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9910&r=gth 
By:  Christian Ewerhart 
Abstract:  It is shown that rentseeking contests with continuous and independent type distributions possess a unique purestrategy Nash equilibrium. 
Keywords:  Rentseeking, private information, purestrategy Nash equilibrium, existence, uniqueness 
JEL:  C7 D7 D8 
Date:  2014–05 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:159&r=gth 
By:  Wolfgang Luhan (Bochum University); Odile Poulsen (University of East Anglia); Michael Roos (Bochum University) 
Abstract:  Fairness considerations are important determinants of behavior in unstructured bargaining situations with equal bargaining power. If the surplus over which the bargaining takes place was created by separate, individual efforts, several entitlementrelated fairness ideals might be relevant. In our experiment we first elicit subjects’ fairness ideals using a questionnaire. In the following production phase each player generates output by luck, individual effort and talent. We analyze whether the elicited fairness ideals guide subjects’ behavior in the subsequent bargaining in which the joint output is distributed among to individuals. We find that bargaining claims deviate significantly from the elicited fairness ideals and are strongly related to performance if one individual had produced more than the partner. These findings contrast the previous literature on fairness ideals, but enrich the findings on selfserving fairness. 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:uea:wcbess:1310&r=gth 
By:  José Manuel, GiménezGómez (Universitat Rovira i Virgili); Antonio, Osorio (Universitat Rovira i Virgili); Josep Enric, Peris (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica) 
Abstract:  Although classic bankruptcy problems take into account a single claims vector, Pulido et al. (2008) show that there are real bankruptcy situations where agents face more than one reference vector. In particular, they consider the claims and an additional reference vector. To analyze these situations, they propose the extreme and the diagonal approaches. Nonetheless, the former approach depends on the order of the vectors: if we interchange the claims and the reference vectors, the result changes. Moreover their study is limited to the case in which the reference vector is lower than the claims vector. In the present note, we propose an extension that solves these shortcomings by introducing the idea of impartiality. 
Keywords:  bankruptcy problems; reference point; compromise solution; impartiality 
JEL:  C71 
Date:  2014–05–20 
URL:  http://d.repec.org/n?u=RePEc:ris:qmetal:2014_002&r=gth 
By:  Ahmet Ozkardas (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université Paris I  PanthéonSorbonne) 
Abstract:  We present a noncooperative unionfirm wage bargaining model in which the union must choose between strike and holdout if a proposed wage contract is rejected. The innovative element that our model brings to the existing literature on wage bargaining, concerns the parties' preferences which are not expressed by constant discount rates, but by sequences of discount factors varying in time. First, we determine subgame perfect equilibria if the strike decision of the union is exogenous. We analyze the case when the union is committed to strike in each disagreement period, the case when the union is committed to strike only when its own offer is rejected, and the case of the never strike exogenous decision. A comparison of the results is provided, among the cases of the exogenous strike decisions. Next, we consider the general model with no assumption on the commitment to strike. We find subgame perfect equilibria in which the strategies supporting the equilibria in the exogenous cases are combined with the minimumwage strategies, provided that the firm is not less patient than the union. If the firm is more impatient than the union, then the firm is better off by playing the noconcession strategy. We find a subgame perfect equilibrium for this case. 
Keywords:  union  firm bargaining ; alternating offers ; varying discount rates ; subgame perfect equilibrium 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:hal00975533&r=gth 
By:  Annarita COLASANTE (Universit… Politecnica delle Marche, Dipartimento di Scienze Economiche e Sociali); Alberto RUSSO (Universit… Politecnica delle Marche, Dipartimento di Scienze Economiche e Sociali) 
Abstract:  This paper analyzes the impact of inequality in the distribution of endowments on contributions. We conduct a lab experiment using the wellknown Public Good Game to test the relation between inequality and contribution to a public fund. We introduce the possibility to choose among three different redistribution rules: equidistribution, proportional to contribution and progressive to endowment. This novelty, combined with a payoff function that depends also on previous period behavior, allows us to verify the hypothesis that players show inequity averse preferences. Results show that inequality has a negative impact on individual contribution. Since inequality is decreasing during repetitions, we deduce that players show inequity averse preferences. 
Keywords:  Inequality, Public Good Game, Reciprocity 
JEL:  C9 D7 H41 
Date:  2014–05 
URL:  http://d.repec.org/n?u=RePEc:anc:wpaper:401&r=gth 