How Noise Creates Diversity express
For a long time, biologists argued: if a herd of animals stably maintains a mix of aggressive and peaceful individuals, does each one alternately change behavior, or do some always fight while others always yield? In classical equations, these options are indistinguishable. The 'Hawks and Doves' game was invented to describe the struggle for prey: hawks fight to the end, doves retreat, avoiding injury.
Physicist Ludwig Boltzmann discovered that disorder (random noise) in any system usually averages everything out. It seemed that in a population, random fluctuations in numbers should gradually erase differences, turning everyone into 'middling' individuals — this idea was dubbed the 'trembling hand' hypothesis. However, a new study showed the opposite: in small groups, noise doesn't blend, it sorts, separating individuals into pure 'hawks' and 'doves' for a long time — like a invisible framework holding the structure. Instead of a homogeneous crowd, a stable diversity emerges.
Randomness, once seen as the destroyer of order, turns out to be its architect. Mathematician John von Neumann, who laid the foundations of game theory, would probably be surprised by this twist: noise not only creates diversity but also guards it.
Original abstract
as written by the authors arXiv:2607.14950
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.
In the 'Hawks and Doves' game, the strategies are named after birds, but it's just an abstraction; in reality, hawks and doves don't play such a game.