Approachability with Constraints

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Abstract. We study approachability in repeated games with vector payoffs, with the additional aspect that there are constraints. Namely, the goal of Player 1 is to approach a given set while ensuring that the realized average payoff in every given stage is not in a given set of payoff vectors that should be evaded. We characterize the pairs of sets (A,E) such that Player 1 can ensure that the long-run average payoff converges to A while evading E.