Cooperation in Prisoners' Dilemmas: the Basic Case of One-shot Prisoners' Dilemmas

As the first book that systematically combines game theory and signal detection theory to provide a foundation for new research, Cooperation in Prisoners' Dilemmas provides a unique perspective on the topic of cooperation in decision making.

This volume shows how contingent cooperators will evolve from any initial population through any payoff monotonic process (like replicator or logistic population dynamics), and remain stable to invasion by other players, including always defecting players. These properties are robust to mimicry and low quality signals, whenever they can be elicited from other players better than pure chance. These properties hold for pure one-shot prisoners' dilemmas: meaning no repeat interactions or information about past behavior is involved, all communication arises only from signals detected after strangers meet the first time; and no subjective preferences for fairness or reciprocity affect the raw dynamics. However, the raw dynamics will evolve such preferences if they motivate players to act contingently toward signals elicited from another player better than pure chance. Finally, the author concludes with derived predictions about the equilibrium frequency of cooperation.