Efficient cooperation by exchanging favors

Wojciech Olszewski, Mikhail Safronov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study chip-strategy equilibria in two-player repeated games. Intuitively, in these equilibria, players exchange favors by taking individually suboptimal actions if these actions create a “gain” for the opponent larger than the player's “loss” from taking them. In exchange, the player who provides a favor implicitly obtains from the opponent a chip that entitles the player to receiving a favor at some future date. Players are initially endowed with a number of chips, and a player who runs out of chips is no longer entitled to receive any favors until she provides a favor to the opponent, in which case she receives one chip back. We show that such simple chip strategies approximate efficient outcomes in a class of repeated symmetric games with incomplete information, in which each player has two possible types, when discounting vanishes. This class includes many important applications, studied in numerous previous papers, such as the favor-exchange model of Möbius (), repeated auctions, and the repeated version of Spulber duopolies of Athey and Bagwell (), among others. We also show the limitation of chip strategies. For example, if players have more than two types, then such simple chip strategies may not approximate efficient outcomes even in symmetric games.

Original languageEnglish (US)
Pages (from-to)1191-1231
Number of pages41
JournalTheoretical Economics
Issue number3
StatePublished - Sep 2018


  • Repeated games
  • chip strategies
  • efficiency

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)


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