On the Computation of Value Correspondence

Recursive game theory provides theoretical procedures for computing the equilibrium payoff sets of repeated games and the equilibrium payoff correspondences of dynamic games. These procedures can not be directly implemented on a computer since, in general, they involve the computation of objects with an infinite cardinality. In the context of repeated games, Conklin, Judd and Yeltekin (2001) emphasize the value of outer and inner approximation schemes that permit both the computation of (approximate) value sets and an estimate of the computational error. In this paper, we propose, and implement outer and inner approximation methods for value correspondences that naturally occur in the analysis of dynamic games. The procedure utilizes set-valued step functions. We provide applications to international lending and a bilateral insurance game with storage