Snowdrift game induces pattern formation in systems of self-propelled particles

TL;DR

This paper explores how self-propelled particles engaged in a snowdrift game form complex spatial and temporal patterns, revealing new feedback mechanisms between game interactions and collective behavior.

Contribution

It introduces a novel combination of active matter and evolutionary game theory, deriving hydrodynamic equations to identify pattern formation regimes in self-propelled systems.

Findings

Identification of parameter regimes with orientational order

Discovery of propagating wave patterns in both species

Confirmation of game-induced pattern formation through simulations

Abstract

Evolutionary games between species are known to lead to intriguing spatio-temporal patterns in systems of diffusing agent. However, the role of inter-species interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active-matter and evolutionary game theory and study a system of two species whose individuals are (self-)propelled and interact through a snowdrift game. We derive hydrodynamic equations for the density and velocity fields of both species from which we identify parameter regimes in which one or both species form macroscopic orientational order as well as regimes of propagating wave patterns. Interestingly, we find simultaneous wave patterns in both species that result from the interplay between alignment and snowdrift interactions - a feedback mechanism that we call game-induced pattern formation. We test these results in agent-based simulations and confirm the different regimes of order and spatio-temporal patterns as well as game-induced pattern formation.