Existence of equilibria in repeated games with long-run payoffs

Galit Ashkenazi-Golan, János Flesch, Arkadi Predtetchinski, Eilon Solan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider repeated games with tail-measurable payoffs, i.e., when the payoffs depend only on what happens in the long run. We show that every repeated game with tail-measurable payoffs admits an ε-equilibrium, for every ε > 0, provided that the set of players is finite or countably infinite and the action sets are finite. The proof relies on techniques from stochastic games and from alternating-move games with Borel-measurable payoffs.

Original languageEnglish
Article numbere2105867119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number11
StatePublished - 15 Mar 2022


FundersFunder number
Abraham Neyman
European Cooperation in Science and Technology
National Natural Science Foundation of China2510/17, 217/17
Israel Science Foundation722/18


    • Nash equilibrium
    • countably many players
    • repeated games
    • tail-measurable payoffs

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