Supergames with States ∗

This paper studies the pure subgame perfect equilibrium outcomes of supergames with finite states and perfect monitoring. First, we define an order-preserving function, which returns payoffs that are one-period incentive compatible. We then use Tarski’s fixed point theorem and the one-stage deviation principle to characterize the average discounted pure subgame perfect equilibrium payoffs as the largest fixed point of this function. We also demonstrate that these equilibrium payoffs can be obtained through iterative application of this function.