Stochastic game

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

Game theoretic analysis of the substitutable product inventory problem with random demands

Abstract: This article uses game theoretic concepts to analyze the inventory problem with two substitutable products having random demands. It is assumed that the two decision makers (players) who make ordering decisions know the substitution rates and the demand densities for both products. Since each player's decision affects the other's single-period expected profit, game theory is used to find the order quantities when the players use a Nash strategy (i.e., they act rationally). We prove the existence and uniqueness of the Nash solution. It is also shown that when one of the players acts irrationally for the sole purpose of inflicting maximum damage on the other, the maximin strategy for the latter reduces to using the solution for the classical single-period inventory problem. We also discuss the cooperative game and prove that the players always gain if they cooperate and maximize a joint objective function.

Wireless information and power transfer in cooperative networks with spatially random relays

Abstract: In this paper, the application of wireless information and power transfer to cooperative networks is investigated, where the relays in the network are randomly located and based on the decode-forward strategy. For the scenario with one source-destination pair, three different strategies for using the available relays are studied, and their impact on the outage probability and diversity gain is characterized by applying stochastic geometry. By using the assumptions that the path loss exponent is two and that the relay-destination distances are much larger than the source-relay distances, closed form analytical results can be developed to demonstrate that the use of energy harvesting relays can achieve the same diversity gain as the case with conventional self-powered relays. For the scenario with multiple sources, the relays can be viewed as a type of scarce resource, where the sources compete with each other to get help from the relays. Such a competition is modeled as a coalition formation game, and two distributed game theoretic algorithms are developed based on different payoff functions. Simulation results are provided to confirm the accuracy of the developed analytical results and facilitate a better performance comparison.

Handbook of game theory with economic applications

Abstract: Preface (R.J. Aumann, S. Hart). Strategic equilibrium (E. van Damme). Foundations of strategic equilibrium (J. Hillas, E. Kohlberg). Incomplete information (R.J. Aumann, A. Heifetz). Non-zero-sum two-person games (T.E.S. Raghavan). Computing equilibria for two-person games (B. von Stengel). Non-cooperative games with many players (M. Ali Khan, Y. Sun). Stochastic games (J-F. Mertens). Stochastic games: recent results (N. Vieille). Game theory and industrial organization (K. Bagwell, A. Wolinsky). Bargaining with incomplete information (L.M. Ausubel, P. Cramton, R.J. Deneckere). Inspection Games (R. Avenhaus, B.V. Stengel, S.Zamir). Economic history and game theory (A. Greif). The shapley value (E. Winter). Variations on the shapley value (D. Monderer, D. Samet). Values of non-transferable utility games (R. McLean). Values of games with infinitely many players (A. Neyman). Values of perfectly competitive economies (S. Hart). Some other economic applications of the value (J-F. Mertens). Strategic aspects of political systems (J. Banks). Game-theoretic analysis of legal rules and institutions (J-P. Benoit, L.A. Kornhauser). Implementation Theory (T. Palfrey). Game Theory and experimental Gaming (M. Shubik).

Dynamic Mechanism Design: A Myersonian Approach

Abstract: We study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods. We make three contributions. First, we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent's equilibrium expected payoff with respect to his current type. It combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by �impulse response functions.� The formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms. Second, we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule (�revenue equivalence�). Third, we characterize perfect Bayesian equilibrium-implementable allocation rules in Markov environments, which yields tractable sufficient conditions that facilitate novel applications. We illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods (�bandit auctions�).