Approachability with constraints

Gaëtan Fournier (1) , Eden Kuperwasser (2) , Orin Munk (2) , Eilon Solan (2) , Avishay Weinbaum (2)

1 AMSE - Aix-Marseille Sciences Economiques
2 TAU - Tel Aviv University

We study approachability theory in the presence of constraints. Given a repeated game with vector payoffs, we study the pairs of sets (A, D) in the payoff space such that Player 1 can guarantee that the long-run average payoff converges to the set A, while the average payoff always remains in D. We provide a full characterization of these pairs when D is convex and open, and a sufficient condition when D is not convex.

Keywords: game theory; approachability; optimization

Domains: Humanities and Social Sciences; Economics and Finance

Gaëtan Fournier, Eden Kuperwasser, Orin Munk, Eilon Solan, Avishay Weinbaum. Approachability with constraints. European Journal of Operational Research, 2021, 292 (2), pp.687-695. ⟨10.1016/j.ejor.2020.11.013⟩. ⟨hal-03138536⟩