Stochastic game

About: Stochastic game is a research topic. Over the lifetime, 9493 publications have been published within this topic receiving 202664 citations.

Forward Induction in the Battle-of-the-Sexes Games

Abstract: This paper provides experimental evidence on forward induction as a refinement criterion. In the basic extensive form, one of the two players chooses to play a battle-of-the-sexes game or to receive a certain payoff. According to forward induction, choosing to play the game is a signal about intended action. Though the presence of the outside option changes play, we find only limited support for the forward-induction hypothesis. The effects of the outside option also reflect the creation of a focal point through the asymmetry created by offering the outside option to one of the two players. (JEL C72)

Games on graphs

Abstract: Evolution occurs in populations of reproducing individuals. The trajectories and outcomes of evolutionary processes depend on the structure of the population. Evolutionary graph theory is a powerful approach to studying the consequences of spatial or social population structure. The vertices of the graph represent individuals. The edges determine who interacts with whom for game payoff and who competes with whom for reproduction. Interaction and competition can be governed by the same graph or by two different graphs. In this paper, we review the basic approach for evolutionary games on graphs and provide new proofs for key results. We formalize the method of identity by descent to derive conditions for strategy selection on finite, weighted graphs. We generalize our results to nonzero mutation rates, and to the case where the interaction and competition graphs do not coincide. We conclude with a perspective of open problems and future directions.

An optimization approach for approximate Nash equilibria

Abstract: In this paper we propose a new methodology for determining approximate Nash equilibria of non-cooperative bimatrix games and, based on that, we provide an efficient algorithm that computes 0.3393- approximate equilibria, the best approximation till now. The methodology is based on the formulation of an appropriate function of pairs of mixed strategies reflecting the maximum deviation of the players' payoffs from the best payoff each player could achieve given the strategy chosen by the other. We then seek to minimize such a function using descent procedures. As it is unlikely to be able to find global minima in polynomial time, given the recently proven intractability of the problem, we concentrate on the computation of stationary points and prove that they can be approximated arbitrarily close in polynomial time and that they have the above mentioned approximation property. Our result provides the best Ɛ till now for polynomially computable Ɛ-approximate Nash equilibria of bimatrix games. Furthermore, our methodology for computing approximate Nash equilibria has not been used by others.

Mechanism design in large games: incentives and privacy

Abstract: We study the problem of implementing equilibria of complete information games in settings of incomplete information, and address this problem using "recommender mechanisms." A recommender mechanism is one that does not have the power to enforce outcomes or to force participation, rather it only has the power to suggestion outcomes on the basis of voluntary participation. We show that despite these restrictions, recommender mechanisms can implement equilibria of complete information games in settings of incomplete information under the condition that the game is large---i.e. that there are a large number of players, and any player's action affects any other's payoff by at most a small amount. Our result follows from a novel application of differential privacy. We show that any algorithm that computes a correlated equilibrium of a complete information game while satisfying a variant of differential privacy---which we call joint differential privacy---can be used as a recommender mechanism while satisfying our desired incentive properties. Our main technical result is an algorithm for computing a correlated equilibrium of a large game while satisfying joint differential privacy. Although our recommender mechanisms are designed to satisfy game-theoretic properties, our solution ends up satisfying a strong privacy property as well. No group of players can learn "much" about the type of any player outside the group from the recommendations of the mechanism, even if these players collude in an arbitrary way. As such, our algorithm is able to implement equilibria of complete information games, without revealing information about the realized types.