Equilibrium in behavior strategies in infinite extensive form games with imperfect information

Summary We prove the existence of equilibrium in behavior strategies for extensive form games when the game has infinite actions. The result is derived under the assumption that the behavior strategies satisfy the bounded measurability condition. The condition implies that the behavior strategies are restricted to those which can be viewed as continuous functions from the set of initial histories to the space of probability distributions over action spaces which satisfy the Lipschitz bound.I am grateful for the helpful comments of an anonymous referee.