EVOLUTIONARY STRATEGY DYNAMICS FOR TAG-BASED COOPERATION AND DEFECTION IN THE SPATIAL AND ASPATIAL SNOWDRIFT GAME

Abstract

Cooperation is a costly behavior undertaken by one individual which benefits another individual. Since cooperators are easily exploited by defectors (those who receive the benefits of cooperation but do not cooperate themselves), the evolution and maintenance of cooperation rely on mechanisms that allow cooperators to interact with one another more frequently than would be predicted based on their relative abundance in a population. One simple mechanism is based on the recognition of "tags" — arbitrary, yet identifiable phenotypic traits. Tags allow for the existence of conditionally cooperative strategies; e.g. individuals could adopt a strategy whereby they cooperate with tag-mates but defect against non-tag-mates. Previous research has considered the tag and strategy dynamics of unconditional and conditional strategies engaged in the Prisoner's Dilemma game, the paradigmatic framework for studying the evolutionary dynamics of cooperation, in which defection against a cooperator yields the greatest fitness payoff, followed by mutual cooperation, mutual defection, and cooperation with a defector. Here, using complementary spatial and aspatial lattice models, an alternative payoff structure is considered, based on the Snowdrift game, in which the rankings of the payoffs associated with mutual defection and cooperation with a defector are reversed relative to the Prisoner's Dilemma. In the absence of mutation, it is demonstrated that the aspatial two-tag game tends to collapse into the traditional, non-tag-based Snowdrift game, with the frequency of cooperators and defectors predicted precisely by evolutionary dynamics analysis. The spatial two-tag game, on the other hand, produces a richer variety of outcomes, whose occurrence depends on the cost-benefit ratio of mutual cooperation; these outcomes include the dominance of conditional cooperators, the dominance of unconditional defectors, and the cyclic (or noncyclic) coexistence of the two. These outcomes are then shown to be modified by mutation (which softens the transition boundaries between outcomes), and by the presence of more than two tags (which promotes nepotistic conditional cooperation).