Stochastic game

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

On relaxation algorithms in computation of noncooperative equilibria

Abstract: This paper considers a special class of numerical algorithms, the so-called relaxation algorithm, for Nash equilibrium points in noncooperative games. The relaxation algorithms have been studied by various authors for the deterministic case. Convergence conditions of this algorithm are based on fixed point theorems. For example, Basar (1987) and Li and Basar (1987) have proved its convergence for a two-player game via the contraction mapping theorem. For the quadratic case these conditions can be easily checked. For other nonlinear payoff functions it is sometimes difficult to check these convergence conditions. In this paper, the authors propose an alternative approach using the residual terms of the Nikaido-Isoda function. The convergence theorem is proved for nonsmooth weakly convex-concave Nikaido-Isoda functions. The family of weakly convex-concave functions is broad enough for applications, since if includes the family of smooth functions. When the payoff functions are twice continuously differentiable, the condition for the residual terms is reduced to strict positiveness of a matrix representing the difference of the Hessians of the Nikaido-Isoda function with respect to the first and second groups of variables. An analogous condition was used by Uryas'ev (1988) to prove convergence of the gradient-type algorithm for the Nash equilibrium problem. In this paper the authors discuss only the deterministic case; nevertheless this approach can be generalized for the stochastic Nash equilibrium problems with uncertainties in parameters. >

An oscillating tragedy of the commons in replicator dynamics with game-environment feedback

Abstract: A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

Game theory and reciprocity in some extensive form experimental games

Abstract: We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

Method of playing a dual wagering game

Abstract: A dual wagering game method for one or more players based on simultaneous participation in two mutually exclusive game components with a payoff being the product of the game component outcomes. Wagers are made in both a repeatable base game component and a nonrepeatable bonus game component which components are mutually exclusive. The outcome of the bonus game component results in a multiplier value. Winnings from repeated plays of the base game component are accumulated until a game ending event occurs and the player receives a payout of any accumulated winnings from the base game component multiplied by the multiplier value determined in the bonus game component.