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 action game can be mimicked by a behavior strategy combination of the infinite action game so that the resulting payoffs from the behavior strategies cannot differ by more than epsilon. Also for every behavior strategy of a player i on a subgame of the infinite action game one can find a behavior strategy of player i of the finite action game which will give expected payoffs that are close to each other on the particular subgame. We use these results to construct E-perfect equilibria of infinite action games. (C) 1999 Elsevier Science S.A. All rights reserved.