Cost Benefits and Cooperation in Spatial Snowdrift Game Agent Systems Approaching Well-Mixed Equilibria

Ken A. Hawick

Keywords

Cost Benefit Analysis, Agent-based Modelling, Snowdrift Game, Spatial Agent

Abstract

Game theory for spatial agents can be usefully compared with quantities measured from direct simulation of spatial agent systems. The Snowdrift game model of a microscopic agent is used to study the approach of actual spatial agent realisations in different dimensions and system geometries with varying numbers of agents in one another's immediate spatial locale. We find that spatial systems of Snowdrift game agents approach the predicted equilibrium behaviour systematically as we increase the neighbourhood size, independent of exact geometry and spatial dimension. We analyse the system in terms of the cost benefit ratio and report on how systems of dimension 2,3,4,5 and with various neighbourhood sizes can be implemented to study the systemic approach to a well-mixed system in a state of dynamic equilibrium.

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