Stochastic game

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

Optimal Learning by Experimentation

Abstract: This paper considers a problem of optimal learning by experimentation by a single decision maker. Most of the analysis is concerned with the characterisation of limit beliefs and actions. We take a two-stage approach to this problem: first, understand the case where the agent's payoff function is deterministic; then, address the additional issues arising when noise is present. Our analysis indicates that local properties of the payoff function (such as smoothness) are crucial in determining whether the agent eventually attains the true maximum payoff or not. The paper also makes a limited attempt at characterising optimal experimentation strategies.

How to Cope with Noise In the Iterated Prisoner's Dilemma

Abstract: Noise in the form of random errors in implementing a choice is a common problem in real-world interactions. Recent research has identified three approaches to coping with noise: adding generosity to a reciprocating strategy; adding contrition to a reciprocating strategy; and using an entirely different strategy, Pavlov, based on the idea of switching choice whenever the previous payoff was low. Tournament studies, ecological simulation, and theoretical analysis demonstrate (1) a generous version of tit-for-tat is a highly effective strategy when the players it meets have not adapted to noise; (2) if the other players have adapted to noise, a contrite version of tit-for-tat is even more effective at quickly restoring mutual cooperation without the risk of exploitation; and (3) Pavlov is not robust.

The determinacy of Blackwell games

Abstract: Games of infinite length and perfect information have been studied for many years. There are numerous determinacy results for these games, and there is a wide body of work on consequences of their determinacy. Except for games with very special payoff functions, games of infinite length and imperfect information have been little studied. In 1969, David Blackwell [1] introduced a class of such games and proved a determinacy theorem for a subclass. During the intervening time, there has not been much progress in proving the determinacy of Blackwell's games. Orkin [17] extended Blackwell's result to a slightly wider class. Blackwell [2] found a new proof of his own result. Maitra and Sudderth [9, 10] improved Blackwell's result in a different direction from that of Orkin and also generalized to the case of stochastic games. Recently Vervoort [18] has obtained a substantial improvement. Nevertheless, almost all the basic questions have remained open. In this paper we associate with each Blackwell game a family of perfect information games, and we show that the (mixed strategy) determinacy of the former follows from the (pure strategy) determinacy of the latter. The complexity of the payoff function for the Blackwell game is approximately the same as the complexity of the payoff sets for the perfect information games. In particular, this means that the determinacy of Blackwell games with Borel measurable payoff functions follows from the known determinacy of perfect information games with Borel payoff sets.