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

Abstract

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.

Neighbourhood, Geometry and Initial Conditional Effects on Fairness and Agent Longevity in Large-Scale SugarScape Models

“…SugarScape with 10% by volume fill of agents initially located randomly on twin-peaked sugar mound distribution on 256 2 model system. tial automata systems such as the Game of Life [16]; the Hawk-Dove model [21]; the Snowdrift model [15]; and cyclic automata [14,20] that can be used to study large scale emergent effects in complex environments.…”

Neighbourhood Size Dependence of Cooperator Cluster Emergence in the Spatial Volunteers' Dilemma

“…Other related game-theoretic models include the Snow-drift model and the Hawk-Dove model [18]. The Snow-drift game model [10] is another interesting theoretical construct that can be used to model the microscopic individual agent behaviour in a spatial agent-based system [34] where many individual agents interact, each with a localised subset of the total number of agents.…”