#### Cooperation Enforcement and Collusion Resistance in Repeated Public Goods Games

##### Kai Li, Dong Hao

Enforcing cooperation among substantial agents is one of the main objectives for multi-agent systems. However, due to the existence of inherent social dilemmas in many scenarios, the free-rider problem may arise during agents' long-run interactions and things become even severer when self-interested agents work in collusion with each other to get extra benefits. It is commonly accepted that in such social dilemmas, there exists no simple strategy for an agent whereby she can simultaneously manipulate on the utility of each of her opponents and further promote mutual cooperation among all agents. Here, we show that such strategies do exist. Under the conventional repeated public goods game, we novelly identify them and find that, when confronted with such strategies, a single opponent can maximize his utility only via global cooperation and any colluding alliance cannot get the upper hand. Since a full cooperation is individually optimal for any single opponent, a stable cooperation among all players can be achieved. Moreover, we experimentally show that these strategies can still promote cooperation even when the opponents are both self-learning and collusive.

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