ON GAMES OF PERFECT INFORMATION: EQUILIBRIA, epsilon-EQUILIBRIA AND APPROXIMATION BY SIMPLE GAMES

We show that every bounded, continuous at infinity game of perfect information has an epsilon-perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing from the original game only on the payoff function. In addition, this approach yields a new characterization of perfect equilibria: A strategy f is a perfect equilibrium in such a game G if and only if it is an 1/n-perfect equilibrium in G(n) for all n, where {G(n)} stands for our approximation sequence.