Noise-Induced Replicator Dynamics in Evolutionary Games

Evolutionary game theory offers a general framework to study how behaviors evolve by social learning in a population. This body of theory can accommodate a range of social dilemmas, or games, as well as real-world complexities such as spatial structures. Nonetheless, this approach typically assumes a deterministic payoff structure for social interactions. Here, we extend evolutionary game theory to accommodate payoffs that fluctuate due to stochastic changes in social conditions. In this setting, the rewards of cooperation or defection may vary over time, even while the underlying mean game remains unchanged. We find that even unbiased environmental noise qualitatively alters evolutionary outcomes. Stochastic payoff fluctuations can stabilize coexistence between cooperators and defectors in the prisoner's dilemma, generate bistability in snowdrift games, and produce stable limit cycles in rock-paper-scissors dynamics-dynamical phenomena that cannot occur under deterministic payoffs. These results demonstrate that environmental variability can fundamentally reshape evolutionary dynamics in a complex but comprehensible way.