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on Game Theory |
| By: | Fedor Sandomirskiy (National Research University Higher School of Economics) |
| Abstract: | We consider repeated zero-sum games with incomplete information on the side of Player 2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value of such an N-stage 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 almost-fair, i.e., if Player 1 forgets his private information the value becomes zero. We describe a class of almost-fair games having bounded values in terms of an easy-checkable property of the auxiliary non-revealing game. We call this property the piecewise property, and it says that there exists an optimal strategy of Player 2 that is piecewise-constant as a function of a prior distribution. Discrete market models have the piecewise property. We show that for non-piecewise almost-fair games with an additional non-degeneracy 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 cycle-free 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 two-person games an alternative characterization of Iterated Kalai-Smorodinsky-Nash Compromise (IKSNC), which was introduced and first characterized by Saglam (2016) for $n$-person games. We present an axiom called Gamma-Decomposability, 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 Gamma-Decomposability 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; Kalai-Smorodinsky 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 re-ductions in the strategy space of individuals in relation to preference announcements. Specifically, it considers the Saijo-type'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 q-mechanisms where q = k + 1. A partially-honest individual is an individual who strictly prefers to tell the truth whenever lying has no effect on her material well-being. When there is at least one partially-honest participant, it offers a necessary condition for Nash implementation by q-mechanisms, called partial-honesty 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 q-mechanism provided that there are at least n - q + 1 partially-honest participants. |
| Keywords: | Nash implementation, partial-honesty, non-connected honesty standards, independent domain, q-mechanisms |
| 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 price-quantity mechanisms in pure exchange economies when agents have intrinsic preferences for responsible-sincerity. An agent has an intrinsic preference for responsible-sincerity if she cares about truth-telling that is in line with the goal of the mechanism designer besides her material well-being. A semi-responsible-sincere agent is an agent who, given what her opponents do, acts in a non-responsible-sincere manner when a responsible-sincere behavior poses obstacles to her material well-being. The class of e¢ cient allocation rules that are Nash implementable is identi.ed provided that there is at least one agent who is semi-responsible-sincere. The Walrasian rule is shown to belong to that class. |
| Keywords: | Nash equilibrium, exchange economies, intrinsic preferences for responsible-sincerity, boundary problem, price-quantity 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 Franche-Comté, CRESE); Sylvain Ferrières (Université de Bourgogne Franche-Comté, CRESE); Eric Rémila (Université de Saint-Etienne, Gate); Phillippe Solal (Université de Saint-Etienne, 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’ stand-alone worths. We call it theproportional Shapley value since it distributes the Harsanyi dividend (Harsanyi, 1959) of all coalitions in proportion to the stand-alone 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 Mas-Colell, 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 well-known 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:2016-08&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 non-members. A model is presented to demonstrate how inequality-averse 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 non-members. 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 non-members is increased. Key Words: self-enforcing agreements; inequality aversion; coalitions; experiments; public goods |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:apl:wpaper:16-09&r=gth |