Efficient cooperation by exchanging favors

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 this kind of 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 games with incomplete information, when discounting vanishes. This class includes many important applications, studied in numerous previous papers, such as the discrete-time favor exchange model of Möbius (2001), repeated auctions, and the repeated Spulber's duopoly of Athey and Bagwell (2001), 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.