Abstract.
Consider an n-person stochastic game with Borel state space S, compact metric action sets A 1,A 2,…,A n , and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a 1,a 2,…,a n ) of the players. If the payoff to each player i is 1 or 0 according to whether or not the stochastic process of states stays forever in a given Borel set G i , then there is an ε-equilibrium for every ε>0.
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AMS (1991) subject classification: 60G40, 91A60, 60E15, 46A55.
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Maitra, A., Sudderth, W. Borel stay-in-a-set games. Int J Game Theory 32, 97–108 (2003). https://doi.org/10.1007/s001820300148
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DOI: https://doi.org/10.1007/s001820300148