Finite and infinite action dynamic games with imperfect information

We show that one can approximate an infinite action game by a finite action game in the sense that every behavior strategy combination of the finite a ction game can be mimicked by a behavior strategy combination of the infini te action game so that the resulting payoffs from the behavior strategies c annot differ by more than epsilon. Also for every behavior strategy of a pl ayer i on a subgame of the infinite action game one can find a behavior str ategy of player i of the finite action game which will give expected payoff s that are close to each other on the particular subgame. We use these resu lts to construct E-perfect equilibria of infinite action games. (C) 1999 El sevier Science S.A. All rights reserved.