Cycles , Diversity and Competition in Rock-Paper-Scissors-Lizard-Spock Spatial Game Agent Simulations

The emergence of complex spatial patterns in agent-based models is closely connected with the symmetries and relationships present between individual microscopic constituents. Games such as Rock-Paper-Scissors (RPS) have a closed cycle relationship amongst players which extends the symmetry. RPS and related games can be played by agents arranged on a spatial grid and have been shown to generate many complex spatial patterns. We consider the implications of extending the individual RPS game complexity to five-cycle games such as “Rock-Paper-ScissorsLizard-Spock” that have competing cyclic reactions. We simulate large spatial systems using a reaction-rate formulation which are simulated for long run times to capture the dynamic equilibrium regime. We report on the stable and unstable phase mixtures that arise in these agent models and comment on the effects that drive them.

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