Existence of equilibria in repeated games with long-run payoffs

G. Ashkenazi-Golan; J. Flesch; A. Predtetchinski; E. Solan

doi:10.1073/pnas.2105867119

Existence of equilibria in repeated games with long-run payoffs

G. Ashkenazi-Golan
, J. Flesch
, A. Predtetchinski
, E. Solan^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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 epsilon-equilibrium, for every epsilon > 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 language	English
Article number	e2105867119
Number of pages	8
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	119
Issue number	11
DOIs	https://doi.org/10.1073/pnas.2105867119
Publication status	Published - 15 Mar 2022

Keywords

repeated games
Nash equilibrium
countably many players
tail-measurable payoffs
2-PLAYER STOCHASTIC GAMES

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10.1073/pnas.2105867119Licence: CC BY-NC-ND

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AU - Flesch, J.

AU - Predtetchinski, A.

AU - Solan, E.

N1 - data source: no data used

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N2 - 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 epsilon-equilibrium, for every epsilon > 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.

AB - 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 epsilon-equilibrium, for every epsilon > 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.

KW - repeated games

KW - Nash equilibrium

KW - countably many players

KW - tail-measurable payoffs

KW - 2-PLAYER STOCHASTIC GAMES

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JF - Proceedings of the National Academy of Sciences of the United States of America

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M1 - e2105867119

ER -

Existence of equilibria in repeated games with long-run payoffs

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Keywords

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