Perturbation theory for games in normal form and stochastic games |
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Authors: | S H Tijs O J Vrieze |
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Institution: | (1) Department of Mathematics, Catholic University, Nijmegen, Holland;(2) Department of Operations Research, Mathematical Center, Amsterdam, Holland |
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Abstract: | In this paper, the effect on values and optimal strategies of perturbations of game parameters (payoff function, transition probability function, and discount factor) is studied for the class of zero-sum games in normal form and for the class of stationary, discounted, two-person, zero-sum stochastic games.A main result is that, under certain conditions, the value depends on these parameters in a pointwise Lipschitz continuous way and that the sets of -optimal strategies for both players are upper semicontinuous multifunctions of the game parameters.Extensions to general-sum games and nonstationary stochastic games are also indicated. |
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Keywords: | Game theory games in normal form stochastic games nonstationary stochastic games perturbation of payoffs perturbation of transition probability function perturbation of discount factor |
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