Robust Evolution Of Contingent Cooperation In Pure One-Shot Prisoners' Dilemmas. Part II: Evolutionary Dynamics & Testable Predictions - Ronald Asher Heiner (Universität des Saarlandes, Center for the Study of Law and Economics (CSLE), 2002)
ROC curves from the signal detection literature are used in an evolutionary analysis of one-shot and repeated prisoners' dilemmas: showing if there is any discounting of future payoffs, or any cost of searching for an additional partner, then cooperative players who contingently participate - in terms of who to play with or when to exit - cannot survive when most other players unconditionally defect; even when contingent participators only interact with themselves by perfectly detecting their own type. However, quite different results hold for players who act contingently, not in terms of whether to play or exit, but rather in terms of how to act with any given partner. There is a form of contingent cooperation in one-shot prisoners' dilemmas (called CD behavior) that will robustly evolve through any payoff monotonic process, such as replicator dynamics. That is, whenever CD-players can detect their own type better than pure chance, they are guaranteed to evolve from any initial population - eventually to a unique evolutionarily stable population composed entirely of contingent cooperators - provided the fear payoff difference is less than the sum of greed and cooperation payoff differences. The adaptive capabilities just described hold for pure one-shot prisoners' dilemmas: meaning no repeated interactions or pairings in any generation are involved; no information or third party reports about past behavior are involved, all signal information arises only from symptoms detected after two strangers meet for the first time; and no subjective preferences for altruism, fairness, equity, reciprocity, or morality affect the raw evolutionary dynamics. Testable predictions are also derived that agree with a large body of experimental data built up since the prisoners dilemma was first introduced in 1950. They describe how the CD-players' equilibrium probability of cooperating changes: depending on the relative size of fear, greed, and cooperation payoff differences; and depending on the players' history of communication, especially when face-to-face discussion is involved.
Keywords: C92; D80; C62; C72; C60; 330; prisoners' dilemma; cooperation; Nash equilibrium; evolutionary stability; replicator dynamics; signal detection; ROC curves; experiment