COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 0000 On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games Johannes Hörner, Satoru Takahashi and Nicolas Vieille February 2012 This paper provides a dual characterization of the limit set of perfect
public equilibrium payoffs in stochastic games (in particular, repeated games) as the
discount factor tends to one. As a first corollary, the folk theorems of Fudenberg, Levine
and Maskin (1994), Kandori and Matsushima (1998) and Hörner, Sugaya, Takahashi and
Vieille (2011) obtain. As a second corollary, in the context of repeated games, it follows
that this limit set of payoffs is a polytope (a bounded polyhedron) when attention is
restricted to equilibria in pure strategies. We provide a two-player game in which this
limit set is not a polytope when mixed strategies are considered. |
