Simpson's Paradox Can Emerge from the N-Player Prisoner's Dilemma: Implications for the Evolution of Altruistic Behavior

Jeff Fletcher and Martin Zwick.

Proceedings of The WorldCongress of the Systems Sciences and ISSS 2000, Allen, J.K. and Wilby, J.M. eds., Toronto, Canada: International Society for the Systems Sciences.

Abstract

Simulations of the n-player Prisoner's Dilemma in multiple populations reveal that Simpson's paradox can emerge in such game-theoretic situations. The relative proportion of cooperators can decrease in each separate sub-population, while the proportion of cooperators in the total population can nonetheless increase, at least transiently. Factors that determine the longevity of this effect are under investigation. The increase of altruistic behavior exhibited in these simulations is not based on reciprocal altruism, as there are no strategies conditional on other players' past actions, nor does it depend on kin selection via inclusive fitness, as there are no genes. This model is very general in that it can represent both biological and social non-zero sum situations in which utility (fitness) depends upon conditions at different hierarchical levels. The two parameters of the prisoner's dilemma in this model, which determine the gain in individual utility for defection and the dependence of utility on collective cooperation, are respectively analogous to within-group and between-group selective forces in multilevel selection theory.