On the limit perfect public equilibrium payoff set in repeated and stochastic games

- We derive a duality-based description of the limit set of PPE payoffs in stochastic games.
- This result readily implies a number of existing folk theorems.
- A second corollary is that the limit set is a polytope under pure strategies.
- This property does not extend when mixed strategies are considered.

This paper provides a dual characterization of the existing ones for the limit set of perfect public equilibrium payoffs in a class of finite stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg et al. (1994), Kandori and Matsushima (1998) and Hörner et al. (2011) obtain. As a second corollary, it is shown that this limit set of payoffs is a convex polytope when attention is restricted to perfect public equilibria in pure strategies. This result fails for mixed strategies, even when attention is restricted to two-player repeated games.