Emergence of polymorphism in stochastic evolutionary games
arXiv:2607.14950
The paper studies how random demographic noise in finite populations can generate and maintain stable mixtures of pure strategies (polymorphism) in the Hawk‑Dove game, showing that stochastic effects can produce long‑lasting polymorphic states despite the trembling‑hand hypothesis.
Abstract
Deterministic evolutionary game theory makes no distinction between a monomorphic population of individuals all of whom share a mixed evolutionarily stable strategy and a polymorphic population of players of pure strategies present in a ratio that reproduces the mixed strategy on average. The so-called trembling hand hypothesis posits that in finite populations demographic noise selects for monomorphism, however, simulation studies have found contradictory results in some situations. Here we resolve this discrepancy by conducting a theoretical analysis of the paradigmatic Hawk-Dove game using timescale separation. We characterise the emergence of polymorphism driven by stochastic effects, finding long-lasting polymorphic states in certain conditions.