Abstract
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 ϵ. 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 ϵ-perfect equilibria of infinite action games.
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