Efficient chip strategies in repeated games

We study a class of chip strategies in repeated games of incomplete information. This class generalizes the strategies studied by Möbius (2001) in the context of a favor-exchange model and the strategies studied in our companion paper Olszewski and Safronov (2017). In two-player games, if players have private values and their types evolve according to independent Markov chains, then under very mild conditions on the stage game, the efficient outcome can be approximated by chip-strategy equilibria when the discount factor tends to 1. We extend this result (assuming stronger conditions) to stage games with any number of players. Chip strategies can be viewed as a positive model of repeated interactions, and the insights from our analysis seem applicable in similar contexts, not covered by the present analysis.