Strategizing against Learners in Bayesian Games
This work addresses strategic interactions in game theory for scenarios involving learning algorithms, with incremental contributions to regret minimization.
The paper tackles the problem of repeated two-player Bayesian games where one player uses no-regret learning and the other is a rational optimizer, aiming to determine the optimizer's minimum guaranteed payoff, identify learning algorithms that cap it, and assess their efficiency, while introducing polytope swap regret as a novel concept.
We study repeated two-player games where one of the players, the learner, employs a no-regret learning strategy, while the other, the optimizer, is a rational utility maximizer. We consider general Bayesian games, where the payoffs of both the optimizer and the learner could depend on the type, which is drawn from a publicly known distribution, but revealed privately to the learner. We address the following questions: (a) what is the bare minimum that the optimizer can guarantee to obtain regardless of the no-regret learning algorithm employed by the learner? (b) are there learning algorithms that cap the optimizer payoff at this minimum? (c) can these algorithms be implemented efficiently? While building this theory of optimizer-learner interactions, we define a new combinatorial notion of regret called polytope swap regret, that could be of independent interest in other settings.