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 transfers into their agents' algorithms, aiming to incentivize behavior in their favor. Our focus is on understanding when players have incentives to make use of monetary transfers, how these payments affect learning dynamics, and what the implications are for welfare and its distribution among the players. We propose a simple game-theoretic model to capture such scenarios. Our results on general games show that in a broad class of games, 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 can reach strong collusive outcomes with low revenue for the auctioneer. These results highlight a challenge for mechanism design in systems where automated learning agents can benefit from interacting with their peers outside the boundaries of the mechanism.