Bryan R. Routledge / Carnegie Mellon University

	Co-Evolution and Spatial Interaction
	Bryan R. Routledge, Carnegie Mellon University
	June 94 - Working Paper
	ABSTRACT This paper investigates the phenomenon of co- evolution. Co-evolution exists when behaviour evolves and agent fitness depends on the evolving behaviour of other agents. An evolutionary model where agents are located on a torus and play repeated prisoner's dilemma games with their immediate neighbours is considered. The evolutionary mechanism uses a genetic algorithm to create strategies using fitness proportional selection, crossover and mutation. The spatial model is exploited by using animation to interpret the results of the simulations. This paper shows that how evolution is modeled affects which Nash equilibrium is selected and, in some cases, determines whether a Nash equilibrium is reached. The number of agents replaced (selecting a new strategy) in a generation modifies the effect of co-evolution and the properties of the evolution system. In the infinitely repeated version of the game, increasing the number of agents replaced reduces the mean and increases the variance of equilibrium population average fitness. In the finitely repeated version, the evolutionary mechanism does not always converge on the unique Nash equilibrium. Using the number of agents replaced per generation, the behaviour of the evolutionary system is classified as Frozen, Critical, Stationary and Converged. Only simulations in the Converged Region achieve the Nash equilibrium. Simulations in the Critical Region do not converge to the Nash equilibrium but are associated with maximal population average fitness as well as non-stationary patterns of average fitnesses and high sensitivity to initial conditions. This last result suggests the possibility of Self-Organized Criticality as an emergent property of the system. Finally, the relationship between this model and that of Kauffman and Johnsen (1991) is used to interpret both our results and theirs.
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	Data updated: 08.01.2002 20:59

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