Refundable Deposits: How to Restore Cooperation in Finitely Repeated Games

Getting self-interested agents to cooperate rather than exploit one another is a central problem wherever autonomous systems interact, and it remains largely open in the setting that matters most for deployed AI: interactions known to end. While infinitely repeated games admit a rich set of Nash equilibria, finitely repeated games typically have much fewer. We show how to restore cooperation in this finitely repeated setting using refundable deposits. In each period a player may place a refundable sum with a neutral intermediary, returned when the game ends and forfeited following a deviation. Paying these deposits is voluntary and incentive compatible at every stage, so no commitment by the players is assumed. The mechanism sustains, as subgame perfect equilibria, payoff profiles that are more efficient than Nash equilibria of the original game, and it needs no transfers between players. We demonstrate it on the prisoner's dilemma and on a congestion game, and discuss its application to populations of interacting AI agents, where a smart contract can serve as the intermediary.