Paying to Do Better: Games with Payments between Learning Agents

In repeated games, such as auctions, players typically use learning algorithms to choose their actions. The use of such autonomous learning agents has become widespread on online platforms. In this paper, we explore the impact of players incorporating monetary transfer policies into their agents' algorithms, aiming to influence behavior in their favor through the dynamics between the agents. Our focus is on understanding when players have incentives to make use of monetary transfers, how such payments may affect learning dynamics, and what the implications are for welfare and its distribution among the players. We propose a simple and general game-theoretic model to capture such scenarios. Our results on general games show that in a very broad class of games, self-interested players benefit from letting their learning agents make payments to other learners during the game dynamics, and that in many cases, this kind of behavior improves welfare for all players. Our results on first- and second-price auctions show that in equilibria of the ``payment policy game,'' the agents' dynamics reach strong collusive outcomes with low revenue for the auctioneer. These results raise new questions and highlight a challenge for mechanism design in systems where automated learning agents can benefit from interacting with their peers in the digital ecosystem and outside the boundaries of the mechanism.

@article{kolumbus2025_2405.20880,
  title={ Paying to Do Better: Games with Payments between Learning Agents },
  author={ Yoav Kolumbus and Joe Halpern and Éva Tardos },
  journal={arXiv preprint arXiv:2405.20880},
  year={ 2025 }
}