Chess-like games may have no uniform Nash equilibria even in mixed strategies
نویسندگان
چکیده
Recently, it was shown that Chess-like games may have no uniform (subgame perfect) Nash equilibria in pure positional strategies. Moreover, Nash equilibria may fail to exist already in two-person games in which all infinite plays are equivalent and ranked as the worst outcome by both players. In this paper, we extend this negative result further, providing examples that are uniform Nash equilibria free even in the (independently) mixed strategies. Given (independently) mixed strategies of all players, we consider two definitions of the corresponding mixed play and effective payoff: given by the Markov or a priori realization.
منابع مشابه
Lecture Notes on Game Theory
1. Extensive form games with perfect information 3 1.1. Chess 3 1.2. Definition of extensive form games with perfect information 4 1.3. The ultimatum game 5 1.4. Equilibria 5 1.5. The centipede game 6 1.6. Subgames and subgame perfect equilibria 6 1.7. Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem 7 2. Strategic form games 10 2.1. Definition 10 2.2. Nash equilibria 10 2.3....
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