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 form 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} stand for our approximation sequence.