APPROXIMATING NASH EQUILIBRIA IN NONZERO-SUM GAMES

Abstract

This paper deals with the approximation of Nash equilibria in m-player games. We present conditions under which an approximating sequence of games admits near-equilibria that approximate near-equilibria in the limit game. We apply the results to two classes of games: (i) a duopoly game approximated by a sequence of matrix games, and (ii) a stochastic game played under the S-adapted information structure approximated by games played over a sampled event tree. Numerical illustrations show the usefulness of this approximation theory.