Excludability and bounded computational capacity

We study the notion of excludability in repeated games with vector payoffs, when one of the players is restricted to strategies with bounded computational capacity. We show that a closed set is excludable by Player 2 when Player 1 is restricted to using only bounded–recall strategies if and only if it does not contain a convex approachable set. We provide partial results when Player 1 is restricted to using strategies that can be implemented by automata.