Well-Mixed Systems and the Approach to Equilibria in Spatial Hawk and Dove Game Simulations

Ken A. Hawick and Chris J. Scogings


Hawk-dove game, Cooperation, Mixed strategy, Stochastic strategy


The Hawk-Dove game is a two-player game-theoretic micro-model that can be used to investigate the evolution of cooperative behaviour in many-agent systems. Individual agents have a stochastic strategy in the form of a continuous-valued probability of playing a non-cooperative hawk' strategy and a large system of agents is formulated on various spatial grids of different dimensionalities and sizes of neighbourhoods. We investigate the approach of the spatial Hawk-Dove game towards a well-mixed equilibrium state as the player interaction neighbourhood size is increased. We explore metrics for assessing the closeness of the system to being well-mixed and compare results from numerical simulations with theoretical predictions for a well-mixed system, where spatial isolation effects ought to be irrelevant.

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