Perfect equilibrium in games with compact action spaces

Simon and Stinchcombe distinguish two approaches to perfect equilibrium, the "trembling hand" approach, and the "finitistic" approach, for games with compact action spaces and continuous payoffs. We investigate relations between the different types of perfect equilibrium introduced by Simon and Stinchcombe. We also propose an improved version of the finitistic approach, and prove existence.Despite the fact that the finitistic approach appeals to basic intuition, our results—specifically Examples 3 and 4—seem to imply a severe critique of this approach. Further examples illustrate the relations between the two approaches and the relation to admissibility of strategies.