Approximating Nash Equilibria in nonzero-Sum Games

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; (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.