The convergence of equilibrium strategies of approximating signaling games

Summary For a class of infinite signaling games, the perfect Bayesian equilibrium strategies of finite approximating games converge to equilibrium strategies of the infinite game. This proves the existence of perfect Bayesian equilibrium for that class of games. It is well known that in general, equilibria may not exist in infinite signaling games.I am very grateful to Karl Iorio with whom I derived most of the results in this paper. I am solely responsible for any remaining errors. I am also grateful to Robert Anderson, Debra Aron, Eddie Dekel, Raymond Deneckere, Michael Kirscheneiter, Steven Matthews, Roger Myerson, Daniel Vincent and Robert Weber for comments on previous drafts of this paper.