WELL-MIXED SYSTEMS AND THE APPROACH TO EQUILIBRIA IN SPATIAL HAWK AND DOVE GAME SIMULATIONS

摘要

The Hawk-Dove game is a two-player game-theoreticrnmicro-model that can be used to investigate the evolutionrnof cooperative behaviour in many-agent systems. Individualrnagents have a stochastic strategy in the form of arncontinuous-valued probability of playing a non-cooperativern“hawk” strategy and a large system of agents is formulatedrnon various spatial grids of different dimensionalities andrnsizes of neighbourhoods. We investigate the approach ofrnthe spatial Hawk-Dove game towards a well-mixed equilibriumrnstate as the player interaction neighbourhood sizernis increased. We explore metrics for assessing the closenessrnof the system to being well-mixed and compare resultsrnfrom numerical simulations with theoretical predictions forrna well-mixed system, where spatial isolation effects oughtrnto be irrelevant.