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

Abstract

Public good scenarios, where shared resources must be managed to best effect, are important applications of agent-based modelling techniques and continue to be a challenge. Models of small numbers of agents and associated theoretical analyses can be insightful, but often large scale simulated systems are needed to capture the spatial and emergent complexities of realistic public goods scenarios. We develop the Volunteers' Dilemma as a spatial agent-based model and explore how it is affected by changes in the temptation for individual agents to defect in groups of differing size. Our game playing group size is controlled by the lattice and neighbourhood geometry used, which we are able to make a parameter of the model through customised software. We explore spatial component cluster statistics for cooperation and defection and discuss their utility in understanding phase transitional behaviour in the model.