Approximating Nash equilibria in nonzero-sum games (Q2701831)

The authors consider an approximation of Nash equilibria in \(m\)-player games. Suppose that \(G\) is a given \(m\)-player game and that the sequence of games \(\{G^n\}\) is a sequence of approximating \(m\)-player games whose limiting game is \(G.\) Conditions under which there exits a sequence of near equilibria in \(\{G^n\}\) that approximates near equilibria in \(G,\) in a sense that is precisely defined in this paper, are derived. The results are applied to two classes of games: (i) a duopoly game that is approximated by a sequence of matrix games and (ii) a stochastic game played under the S-shaped information structure that is approximated by games that are played over a sampled event tree. The section on numerical illustration demonstrates the usefulness of this approach.