Stochastic Games on a Product State Space
AbstractWe examine product-games, which are n-player stochastic games satisfying: (1) the state space is a product S(1)Ãâ¦ÃS(n); (2) the action space of any player i only depends of the i-th coordinate of the state; (3) the transition probability of moving from s(i) ∈ S(i) to t(i) ∈S(i), on the i-th coordinate S(i) of the state space, only depends on the action chosen by player i. So, as far as the actions and the transitions are concerned, every player i can play on the i-th coordinate of the product-game without interference of the other players. No condition is imposed on the payoff structure of the game. We focus on product-games with an aperiodic transition structure, for which we present an approach based on so-called communicating states. For the general n-player case, we establish the existence of 0-equilibria, which makes product-games one of the first classes within n-player stochastic games with such a result. In addition, for the special case of two-player zero-sum games of this type, we show that both players have stationary 0-optimal strategies. Both proofs are constructive by nature.
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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 010.
Date of creation: 2007
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Economics (Jel: A);
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-04-28 (All new papers)
- NEP-GTH-2007-04-28 (Game Theory)
- NEP-MIC-2007-04-28 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Flesch, J. & Thuijsman, F. & Vrieze, O.J., 2007. "Stochastic games with additive transitions," European Journal of Operational Research, Elsevier, vol. 179(2), pages 483-497, June.
- Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
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