Professor Heiner continues writing a book about players who cooperate contingently in one-shot Prisoners’ Dilemmas, depending on signals detected while communicating with their partners. His analysis generalizes signal detection theory from behavioral psychology, by allowing simultaneously shifting signal distributions, caused by contingent cooperators detecting signals more or less cautiously (which affects their probability of cooperating with other players). His analysis shows how the probability of cooperating depends on the four prisoners’ dilemma payoffs: the “temptation payoff” (T) when one player defects on another player’s cooperation, the “cooperation payoff” (R) when both players cooperate, the “penalty payoff” (P) when both players defect, and the “sucker’s payoff” (S) when one player’s cooperation is defected on by another player.
Professor Heiner’s analysis implies stable Nash equilibria always exist that enable contingent cooperators to grow within the whole population against always defecting players. Testable predictions can then be derived: – about when contingent players will cooperate more or less frequently under alternative signal detection conditions (over the full range from perfect to random detection) – and for alternative payoff conditions, where the cooperation payoff difference (R - P) increases or decreases relative to the greed and fear payoff differences (T - R) and (P - S). By comparison, standard game theory can only predict zero probability of cooperation in one-shot prisoners’ dilemmas, regardless of any potential signal detection or payoff conditions – so long as the payoff ranking (T > R > P > S) is preserved.
Professor Heiner has also written the following journal articles: 1. “Robust Contingent Cooperation in Pure One-Shot PD’s.”
Under another revision for Nature. Below is the opening paragraph.
Signal detection theory is used to derive new results about stability and dynamics toward cooperation. I here show contingent cooperators will evolve from any initial population through any payoff monotonic process (including replicator and logistic population dynamics). These properties are robust to signaling and communication costs between players, including mimicry and low-quality signals weakly correlated with a player’s behavior. Signaling is also shown to have the same causal basis as that used in the natural sciences to forecast future events. The limiting case of pure chance detection is also considered; showing that even here, contingent cooperators can have a competitive advantage. These results hold for pure one–shot prisoners’ dilemmas: meaning no repeated interactions and no information about past behavior is involved, all communication arises only from signals detected after two strangers meet for the first time; and no subjective preferences for fairness or reciprocity affect the raw evolutionary dynamics. I also describe testable predictions about the contingent cooperators’ frequency of cooperation.
3. “Expected Utility & Subjective Probability Axioms For N-Player Causal Games”
Revised for the Journal of Game Theory. This paper generalizes earlier expected utility axioms by Savage and Fishburn – allowing past events to causally influence a decision maker’s preferences and beliefs.
4. “Extending Game Trees to Causal Networks”
Now being revised for the Journal of Economic Theory. This paper uses graph theory mathematics to extend game tree diagrams to a more general form, called a causal network. Causal networks allow new predictions for rational behavior in a variety of cooperation versus conflict situations, including one-shot prisoners’ dilemmas.