Self-Evident Sets and the Value of Linking

We propose a theory of linking in repeated games based on the notion of self-evident sets, which describes what becomes "public" at the end of a stage-game where players observe both public and private information. For any stage game we obtain a tight bound on the average per-period efficiency loss needed to strictly enforce a stage-game outcome throughout a T-period repeated game when T is large. Our results apply to all monitoring structures (public and private) and strategy profiles (pure and correlated). They explain the inefficiency result in Abreu, Milgrom and Pearce (1991), as well as the approximate-efficiency results in Compte (1998), Obara (2008), and Chan and Zhang (2016)