Limits of correlation in repeated games with bounded memory

Gilad Bavly; Ron Peretz

doi:10.1016/j.geb.2019.03.003

Limits of correlation in repeated games with bounded memory

Gilad Bavly, Ron Peretz

Department of Economics

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

4 Scopus citations

Abstract

We study repeated games in which each player i is restricted to (mixtures of) strategies that can recall up to k _i stages of history. Characterizing the set of equilibrium payoffs boils down to identifying the individually rational level (“punishment level”) of each player. In contrast to the classic folk theorem, in which players are unrestricted, punishing a bounded player may involve correlation between the punishers’ actions. We show that the extent of such correlation is at most proportional to the ratio between the recall capacity of the punishers and the punishee. Our result extends to a few variations of the model, as well as to finite automata.

Original language	English
Pages (from-to)	131-145
Number of pages	15
Journal	Games and Economic Behavior
Volume	115
DOIs	https://doi.org/10.1016/j.geb.2019.03.003
State	Published - May 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Funding

We thank Yuval Heller and Eilon Solan for helpful suggestions. G. Bavly acknowledges support from the Department of Economics at Bar-Ilan University, the Sir Isaac Wolfson Chair in Economics and Business Administration, ISF grants 1188/14 and 1626/18, and ERC starting grant #677057. We would like to thank two anonymous referees and an AE for many helpful comments. We thank Yuval Heller and Eilon Solan for helpful suggestions. G. Bavly acknowledges support from the Department of Economics at Bar-Ilan University , the Sir Isaac Wolfson Chair in Economics and Business Administration , ISF grants 1188/14 and 1626/18 , and ERC starting grant # 677057 . We would like to thank two anonymous referees and an AE for many helpful comments.

Funders	Funder number
Department of Economics at Bar-Ilan University
Economics and Business Administration
Horizon 2020 Framework Programme	677057
H2020 European Research Council
Iowa Science Foundation
European Commission
Bar-Ilan University
Israel Science Foundation	1188/14, 1626/18

Keywords

Bounded complexity
Bounded recall
Concealed correlation
Equilibrium payoffs
Finite automata
Repeated games

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10.1016/j.geb.2019.03.003

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Limits of correlation in repeated games with bounded memory

Abstract

Bibliographical note

Funding

Keywords

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