Iterated Prisoner’s Dilemma with a Group of Grims by Chan Lee ’24

Iterated Prisoner’s Dilemma with a Group of Grims by Chan Lee ’24, Wednesday May 8, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Thesis

Abstract: Despite mutual defection being the only Nash equilibrium in the one-shot Prisoner’s Dilemma, it has been shown that cooperation could emerge if the game is played repeatedly.  We study whether this phenomenon could occur if a rational agent with imperfect information played the Iterated Prisoner’s Dilemma with a community of individuals who each adopt the grim trigger strategy. We prove that if the agent plays for infinitely many rounds and is blind (does not know whether their opponent in any round has been triggered) and informed (knows how many are triggered in the community), then the size of the payoff for mutual cooperation and the number of triggered grims in the community determine whether it is optimal to cooperate or to defect indefinitely. We also show that if the agent is not blind and plays for infinitely many rounds, then only the payoff for mutual cooperation determines whether it is optimal to defect indefinitely or not. Lastly, we reveal that the optimal strategy for playing finitely many rounds is to potentially cooperate for the first few rounds and defect for the rest.