We study anonymous repeated games where players may be “commitment types” who always take the same action. We establish a stark anti-folk theorem: if the distribution of the number of commitment types satisfies a smoothness condition and the game has a “pairwise dominant” action, this action is almost always taken. This implies that cooperation is impossible in the repeated prisoner's dilemma with anonymous random matching. We also bound equilibrium payoffs for general games. Our bound implies that industry profits converge to zero in linear-demand Cournot oligopoly as the number of firms increases.

We prove the folk theorem for discounted repeated games with anonymous random matching. We allow non‐uniform matching, include asymmetric payoffs, and place no restrictions on the stage game other than full dimensionality. No record‐keeping or communication devices—including cheap talk communication and public randomization—are necessary.

We construct a dynamic model of election campaigns. In the model, opportunities for candidates to refine/clarify their policy positions are limited and arrive stochastically along the course of the campaign until the predetermined election date. We show that this simple friction leads to rich and subtle campaign dynamics. We first demonstrate these effects in a series of canonical static models of elections that we extend to dynamic settings, including models with valence and a multidimensional policy space. We then present general principles that underlie the results from those models. In particular, we establish that candidates spend a long time using ambiguous language during the election campaign in equilibrium.