
on Game Theory 
By:  Fedor Sandomirskiy (National Research University Higher School of Economics) 
Abstract:  We consider repeated zerosum games with incomplete information on the side of Player 2 with the total payoff given by the nonnormalized sum of stage gains. In the classical examples the value of such an Nstage game is of the order of N or of square root of N, as N tends to infinity. Our aim is to find what is causing another type of asymptotic behavior of the value observed for the discrete version of the financial market model introduced by De Meyer and Saley. For this game Domansky and independently De Meyer with Marino found that the value remains bounded, as N tends to infinity, and converges to the limit value. This game is almostfair, i.e., if Player 1 forgets his private information the value becomes zero. We describe a class of almostfair games having bounded values in terms of an easycheckable property of the auxiliary nonrevealing game. We call this property the piecewise property, and it says that there exists an optimal strategy of Player 2 that is piecewiseconstant as a function of a prior distribution. Discrete market models have the piecewise property. We show that for nonpiecewise almostfair games with an additional nondegeneracy condition the value is of the order of squarte root of N 
Keywords:  repeated games with incomplete information, error term, bidding games, piecewise games, asymptotics of the value 
JEL:  C73 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:hig:wpaper:148/ec/2016&r=gth 
By:  Anna Khmelnitskaya (St.Petersburg State University, Russia); Gerard van der Laan (VU University Amsterdam, the Netherlands); Dolf Talman (Tilburg University, the Netherlands) 
Abstract:  In this paper we introduce two values for cooperative games with communication graph structure. For cooperative games the shapley value distributes the worth of the grand coalition amongst the players by taking into account the worths that can be obtained by any coalition of players, but does not take into account the role of the players when communication between players is restricted. Existing values for communication graph games as the Myerson value and the average tree solution only consider the worths of connected coalitions and respect only in this way the communication restrictions. They do not take into account the position of a player in the graph in the sense that, when the graph is connected, in the unanimity game on the grand coalition all players are treated equally and so players with a more central position in the graph get the same payoff as players that are not central. The two new values take into account the position of a player in the graph. The first one respects centrality, but not the communication abilities of any player. The second value reflects both centrality and the communication ability of each player. That implies that in unanimity games players that do not generate worth but are needed to connect worth generating players are treated as those latter players, and simultaneously players that are more central in the graph get bigger shares in the worth than players that are less central. For both values an axiomatic characterization is given on the class of connected cyclefree graph games. 
Keywords:  cooperative game; Shapley value; communication graph; restricted cooperation; centrality 
JEL:  C71 
Date:  2016–09–02 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20160070&r=gth 
By:  Saglam, Ismail 
Abstract:  In this paper, we offer for twoperson games an alternative characterization of Iterated KalaiSmorodinskyNash Compromise (IKSNC), which was introduced and first characterized by Saglam (2016) for $n$person games. We present an axiom called GammaDecomposability, satisfied by any solution that is decomposable with respect to a given reference solution Gamma. We then show that the IKSNC solution is uniquely characterized by GammaDecomposability whenever Gamma satisfies the standard axioms of Independence of Equivalent Utility Representations and Symmetry, along with three additional axioms, namely Restricted Monotonicity of Individually Best Extensions, Weak Independence of Irrelevant Alternatives, and Weak Pareto Optimality under Symmetry. 
Keywords:  Cooperative bargaining; KalaiSmorodinsky solution; Nash solution 
JEL:  C71 C78 
Date:  2016–09–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:73564&r=gth 
By:  Lombardi, Michele; Yoshihara, Naoki 
Abstract:  This paper investigates the robustness of Dutta and Sen's (2012) Theorem 1 to reductions in the strategy space of individuals in relation to preference announcements. Specifically, it considers the Saijotype's (1988) simplification of Maskin's canonical mechanism, according to which each individual's strategy choice includes her own preference and those of her k ‘neighbor’ individuals. This paper refers to this type of mechanisms as qmechanisms where q = k + 1. A partiallyhonest individual is an individual who strictly prefers to tell the truth whenever lying has no effect on her material wellbeing. When there is at least one partiallyhonest participant, it offers a necessary condition for Nash implementation by qmechanisms, called partialhonesty monotonicity, and shows that in an independent domain of preferences that condition is equivalent to Maskin monotonicity. It also shows that the limitations imposed by Maskin monotonicity can be circumvented by a qmechanism provided that there are at least n  q + 1 partiallyhonest participants. 
Keywords:  Nash implementation, partialhonesty, nonconnected honesty standards, independent domain, qmechanisms 
JEL:  C72 D71 D82 
Date:  2016–08 
URL:  http://d.repec.org/n?u=RePEc:hit:hituec:651&r=gth 
By:  Lombardi, Michele; Yoshihara, Naoki 
Abstract:  We study Nash implementation by natural pricequantity mechanisms in pure exchange economies when agents have intrinsic preferences for responsiblesincerity. An agent has an intrinsic preference for responsiblesincerity if she cares about truthtelling that is in line with the goal of the mechanism designer besides her material wellbeing. A semiresponsiblesincere agent is an agent who, given what her opponents do, acts in a nonresponsiblesincere manner when a responsiblesincere behavior poses obstacles to her material wellbeing. The class of e¢ cient allocation rules that are Nash implementable is identi.ed provided that there is at least one agent who is semiresponsiblesincere. The Walrasian rule is shown to belong to that class. 
Keywords:  Nash equilibrium, exchange economies, intrinsic preferences for responsiblesincerity, boundary problem, pricequantity mechanism 
JEL:  C72 D71 
Date:  2016–08 
URL:  http://d.repec.org/n?u=RePEc:hit:hituec:649&r=gth 
By:  Sylvain Béal (Université de Bourgogne FrancheComté, CRESE); Sylvain Ferrières (Université de Bourgogne FrancheComté, CRESE); Eric Rémila (Université de SaintEtienne, Gate); Phillippe Solal (Université de SaintEtienne, Gate) 
Abstract:  We introduce a non linear weighted Shapley value for cooperative games with transferable utility,in which the weights are endogenously given by the players’ standalone worths. We call it theproportional Shapley value since it distributes the Harsanyi dividend (Harsanyi, 1959) of all coalitions in proportion to the standalone worths of its members. We show that this value recommends an appealing payoff distribution in a land production economy introduced in Shapley and Shubik (1967). Although the proportional Shapley value does not satisfy the classical axioms of linearity and consistency (Hart and MasColell, 1989), the main results provide comparable axiomatic characterizations of our value and the Shapley value by means of weak versions of these two axioms. Moreover, our value inherits several wellknown properties of the weighted Shapley values. 
Keywords:  (Weighted) Shapley value, proportionality, Harsanyi dividends, potential, land production economy 
Date:  2016–08 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:201608&r=gth 
By:  David M. McEvoy; John K. Stranlund 
Abstract:  We explore the formation of coalitions to provide a public good when some players are averse to payoff inequality between coalition members and nonmembers. A model is presented to demonstrate how inequalityaverse preferences could cause players to deliberately block profitable but inequitable coalitions from forming, and how the likelihood of such blocks is affected by the magnitude of payoff inequality. We then empirically examine coalition formation rates using laboratory experiments. Our results show that profitable coalitions are less likely to form the bigger the gap in payoffs between members and freeriding nonmembers. The experimental design allows us to tease out potentially confounding effects between the level of inequality and the minimum number of players required to make the coalition profitable. As predicted, controlling for the size of the participation threshold, we find that coalition formation rates fall as the payoff gap between members and nonmembers is increased. Key Words: selfenforcing agreements; inequality aversion; coalitions; experiments; public goods 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:apl:wpaper:1609&r=gth 