Existence of equilibria in repeated games with long-run payoffs

Galit Ashkenazi-Golan; János Flesch; Arkadi Predtetchinski; Eilon Solan

doi:10.1073/pnas.2105867119

Existence of equilibria in repeated games with long-run payoffs

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

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › 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 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 language	English
Article number	e2105867119
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
State	Published - 15 Mar 2022

Keywords

Nash equilibrium
countably many players
repeated games
tail-measurable payoffs

All Science Journal Classification (ASJC) codes

General

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10.1073/pnas.2105867119

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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 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.",

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AU - Ashkenazi-Golan, Galit

AU - Flesch, János

AU - Predtetchinski, Arkadi

AU - Solan, Eilon

PY - 2022/3/15

Y1 - 2022/3/15

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 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.

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 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.

KW - Nash equilibrium

KW - countably many players

KW - repeated games

KW - tail-measurable payoffs

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

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

IS - 11

M1 - e2105867119

ER -

Existence of equilibria in repeated games with long-run payoffs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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