Econometrica: Mar, 2005, Volume 73, Issue 2

Belief‐Free Equilibria in Repeated Games

https://doi.org/10.1111/j.1468-0262.2005.00583.x
p. 377-415

Jeffrey C. Ely, Johannes Hörner, Wojciech Olszewski

We introduce a class of strategies that generalizes examples constructed in two‐player games under imperfect private monitoring. A sequential equilibrium is if, after every private history, each player's continuation strategy is optimal independently of his belief about his opponents' private histories. We provide a simple and sharp characterization of equilibrium payoffs using those strategies. While such strategies support a large set of payoffs, they are not rich enough to generate a folk theorem in most games besides the prisoner's dilemma, even when noise vanishes.