Eco-evolutionary games in noisy environments

Cooperative and competitive interactions among individuals harvesting resources can shape environmental states, such as prey abundance. In turn, environmental conditions feed back to influence strategic interactions. Eco-evolutionary game theory studies how these feedbacks shape the co-evolution of behavior and environment. Existing models typically assume deterministic, noise-free environmental dynamics. However, real environments are inherently stochastic, for example due to finite resources, and noise can qualitatively alter social outcomes. Here, we incorporate stochastic environmental dynamics into eco-evolutionary game theory. When environmental change is slow relative to strategy updates, we show that behavior reflects a mixture of the games associated with low and high environmental states, often yielding outcomes qualitatively distinct from deterministic predictions. In particular, environmental stochasticity can eliminate bistability and enforce dominance of a single behavior. When environmental dynamics are faster, populations have less opportunity to track fluctuations, and behavior converges toward strategies that are optimal on average. Stochasticity can even causes persistent oscillations in the tragedy of commons, in regimes where classical models predict stability. Our framework provides a tractable approach for analyzing social behavior linked to environmental dynamics how noise shapes long-term eco-evolutionary outcomes.