Complex Domain Layering in Even-Odd Cyclic State Rock-Paper-Scissors Game Simulations

Models based on spatial game theory continue to attract interest as platforms for studying complex simulations such as ecological, socio-political and networked-agent systems. The well-known rock-paper-scissors game is one such model that can be played out by networked agents with individual strategies competing against their spatially-connected sites. Stochastic simulations of this 3-state game can be used to model discretely the chemical or organisational rate equations that would normally require continuous numerical methods. In this paper we study higher numbers of states and the interplay between cyclic interactions amongst the species. We find a complex domain layering pattern that varies with the even/oddness of the number of states and we use visualisation and statistical simulation techniques to explore this behaviour. We find that the vacant sites in the spatial model play a subtle and important role in controlling species population levels.

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