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Significance Nash equilibrium, of central importance in strategic game theory, exists in all finite games. Here we prove that it exists also in all infinitely repeated games, with a finite… Click to show full abstract
Significance Nash equilibrium, of central importance in strategic game theory, exists in all finite games. Here we prove that it exists also in all infinitely repeated games, with a finite or countably infinite set of players, in which the payoff function is bounded and measurable and the payoff depends only on what is played in the long run, i.e., not on what is played in any fixed finite number of stages. To this end we combine techniques from stochastic games with techniques from alternating-move games with Borel-measurable payoffs.
Journal Title: Proceedings of the National Academy of Sciences of the United States of America
Year Published: 2022
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