When is the reservation value in a repeated game equal to the minmax payoff?

We study the relationship between a player’s minmax payoff and his lowest equilibrium payoff (his reservation utility) in repeated games with imperfect monitoring. We provide a necessary and sufficient condition on the information structure under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show that, if the monitoring structure of an infinitely repeated game ‘nearly’ satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.