Uniqueness of Oblivious Equilibrium in Dynamic Discrete Games∗

The recently introduced concept of oblivious equilibrium aims at approximating Markov-Perfect Nash Equilibria (MPNE) when its calculation is computationally prohibitive in Ericson-Pakes-style games with many players. This paper examines and extends the oblivious equilibrium concept to dynamic discrete choice games. We consider a set of assumptions commonly posed in the applied dynamic games literature and establish oblivious equilibrium properties. In contrast to Ericson-Pakes models, we find that there is a unique oblivious equilibrium in the dynamic game for any number of players under the frequently posed assumption of independence of state transitions across players. We demonstrate that the distance between this equilibrium and any MPNE converges in probability to zero as the number of game players goes to infinity. Unlike the original work on oblivious equilibrium, our convergence result requires neither a "light tail" condition nor the absence of aggregate state variables.