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.

翻译：在重复博弈（如拍卖）中，参与者通常使用学习算法来选择其行动。此类自主学习智能体的应用已在在线平台上变得十分普遍。本文探讨了参与者将货币转移机制纳入其智能体算法所产生的影响，旨在激励对自身有利的行为。我们重点关注参与者何时有动机利用货币转移、这些支付如何影响学习动态，以及对整体福利及其在参与者间分配的启示。为此，我们提出了一个简单的博弈论模型来刻画此类场景。我们在一般博弈上的结果表明，在广泛的博弈类别中，参与者允许其学习智能体在博弈动态过程中向其他学习智能体进行支付是有益的，并且在许多情况下，此类行为能提升所有参与者的福利。针对第一价格与第二价格拍卖的研究结果显示，在“支付策略博弈”的均衡中，智能体的动态可能达成强合谋结果，导致拍卖者收益低下。这些结果凸显了机制设计面临的一个挑战：在自动化学习智能体能够通过与机制边界外的其他智能体互动而获益的系统中，传统机制可能面临失效风险。