A successful strategy for iterated Prisoner's dilemma with any number of channels

Iterated Prisoner's Dilemma (IPD) and its variants are widely used models for studying cooperation in human societies and AI systems. This paper focuses on multichannel IPD with any finite number of channels, and examines how an agent can achieve generally high payoffs in this setting. We introduce a novel strategy that bases its decision to cooperate or defect on the difference in the cumulative number of defections between two agents. We show that this strategy naturally possesses niceness, retaliation, and forgiveness. Moreover, we theoretically analyze the performance of our proposed strategy across various scenarios, including self-play with and without errors, as well as against a diverse range of opponent strategies. Notably, we show that our strategy is invincible, ensuring that it never receives a lower expected payoff than any opponent strategy. Lastly, we show that our strategy is stable, in terms of constituting an (approximate) Nash equilibrium or subgame perfect equilibrium, under self-play conditions. Extensive simulations empirically validate the evolutionary advantages of our strategy, and showcase its potential to facilitate the emergence and sustainment of cooperation.