NEIGHBOURHOOD SIZE DEPENDENCE OF COOPERATOR CLUSTER EMERGENCE IN THE SPATIAL VOLUNTEERS’ DILEMMA Ken A. Hawick Department of Computer Science, University of Hull, Cottingham Road, Hull HU6 7RX, UK. Email: k.a.hawick@hull.ac.uk, Tel: +44 01482 465181 Fax: +44 01482 466666 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 asso- ciated theoretical analyses can be insightful, but often large scale simulated systems are needed to capture the spatial and emergent complexities of realistic public goods sce- narios. We develop the Volunteers’ Dilemma as a spa- tial 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 compo- nent cluster statistics for cooperation and defection and discuss their utility in understanding phase transitional be- haviour in the model. KEY WORDS Spatial game theory; volunteers’ dilemma; agent-based model; complex system; emergence. 1 Introduction Game theory has proved a valuable tool for under- standing the complex phenomena that occur in sociologi- cal [3] and interactive systems. Spatial games played with individual agents that are constrained to interact with their local neighbours on, for example, a lattice can be especially revealing as they allow individual spatial regions to mani- fest different behaviours and to interact - much as real an- imals or people do in sociological settings [22]. Such spa- tial models go beyond theoretical analyses and can capture fluctuations and other details not possible in a mean-field approach. Game theory and game models arise in a number of contexts including physical [11] and sociological systems [9]. Game theory [27, 30] makes a number of predictions concerning the behaviour of agents interacting in a spatial system [25]. Cooperation [4, 20, 26] is an important trait in agent-based systems and the study of the emergence [29] or suppression of cooperation in a complex system of many independent agents is an important area. Spatial emergence can be modelled using a game theoretic formulation [30] such as the iterated spatial prisoners’ dilemma [27, 28]. Figure 1. Growth of region of (red) defection on a hexago- nal mesh, showing the largest cluster of defectors outlined in black against a background of blue cooperator/volun- teers. This scenario is based on the well-known two-player pris- oners’ dilemma [4]. The Prisoners’ Dilemma is well known and has had much related work on it reported in the liter- ature. An interesting variant is the Volunteers’ Dilemma, which has a more asymmetric character and models public goods situations [2, 8, 23] such as human volunteers or for example prairie dog groups where one has to “volunteer” to be a lookout - at some cost to the individual [36], but at huge public good to the group. Figure 1 shows our implementation of the spatial Vol- unteers’ Dilemma on a hexagonal mesh with red defector agents encroaching upon a background of blue cooperators, with the largest cluster of defectors outlined in black. 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 theoret- ical construct that can be used to model the microscopic individual agent behaviour in a spatial agent-based sys- tem [34] where many individual agents interact, each with a localised subset of the total number of agents. We describe this subset as their localised neighbourhood. The Prison- Proceedings of the IASTED International Conference Modelling and Simulation (AfricaMS 2014) September 1 - 3, 2014 Gaborone, Botswana DOI: 10.2316/P.2014.813-020 87