Approachability with Constraints

TL;DR

This paper extends approachability theory to constrained settings, characterizing conditions under which a player can ensure convergence to a target set while maintaining payoffs within constraints in repeated games.

Contribution

It introduces a framework for approachability with constraints, providing a characterization of feasible pairs of target and constraint sets in vector payoff spaces.

Findings

Characterization of feasible (A,D) pairs for approachability with constraints

Conditions under which Player 1 can guarantee convergence within constraints

Extension of classical approachability theory to constrained scenarios

Abstract

We study approachability theory in the presence of constraints. Given a repeated game with vector payoffs, we characterize 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.