  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.
