The Center for Study of Public Choice
Economics Department

Ronald A. Heiner


Dr. Heiner continued his research on the evolution of cooperation, combining standard game theory with signal detection theory from behavioral psychology. He is currently finishing a book titled Cooperation in Prisoners' Dilemmas: the Critical Case of One-Shot Interactions (World Scientific Press). During last year, Dr. Heiner solved certain problems about how to combine signal detection analysis with standard game theory.

Standard game theory assumes individual players of a given type will behave in the same way - including all the contingent cooperators in a larger population that also includes always defecting players. However, an individual player could still behave contingently (and thus is still part of the contingently cooperative sub-population) - yet reduce its probability of cooperating - by choosing to detect signals from its partner more cautiously than another contingent cooperator.

Such a more cautious contingent cooperator may also have higher expected payoff than less cautious ones (causing more cautious contingent cooperators to grow faster than less cautious ones) - thereby destabilizing behavior within the contingently cooperative sub-population. Eventually, such instability might lead all the continent cooperators to become totally cautious and thereby never cooperate. Similar "unraveling" within a given sub-population is possible in many game theory models (an unsolved issue in standard literature).

Dr. Heiner has developed a more general version of signal detection theory - allowing for simultaneously shifting signal distributions - caused by choosing to detect signals more cautiously, as noted above. On the other hand, standard signal detection theory assumes players' signal distributions remain fixed as they vary their degree of caution in detecting signals.

The generalized signal detection analysis implies there will always exist a unique Nash equilibrium within the contingently cooperative sub-population: where all continent cooperators choose to be equally cautious in detecting signals from their partners. So no continent cooperator can benefit from unilaterally becoming more cautious in detecting signals. The resulting stable Nash equilibrium among continent cooperators guarantees they will grow until they take over the whole population, eventually cooperating at the maximum frequency possible without being outperformed by always defecting players.

Dr. Heiner is finishing revisions from the editor's comments, about the generalized signal detection analysis, and the resulting implications that establish stable cooperation (within the contingently cooperative sub-population) in one-shot prisoners' dilemmas.

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