Spatial Evolution of Automata in the Prisoners' Dilemma

Oliver Kirchkamp

Abstract:

The paper applies the idea of evolution to a spatial model. We assume that prisoners' dilemmas or coordination games are played repeatedly within neighborhoods where players do not optimize but instead copy successful strategies.

Discriminatory behavior of players is introduced representing strategies as small automata, identical for a player but possibly in different states against different neighbors. Extensive simulations show that cooperation persists even in a stochastic environment and that success among surviving strategies may differ. We present a simple analytical model that explains the latter phenomenon.

Behavior in coordination games follows neither Pareto nor risk dominance but can be explained by a simple analytical model of evolution of clusters.

• Keywords: Evolutionary Game Theory, Networks, Prisoners' Dilemma, Overlapping Generations.
• JEL-Code: C63, C73, D62, D83, R12, R13.

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Click here for a copy of the paper as a PDF file (2484081 bytes, 50 pages).

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A more recent version of the paper (as of June 30, 1999, 1536406 bytes, 39 pages) can be found here.

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Meanwhile, the paper has been published as

• Oliver Kirchkamp (2000), “Spatial Evolution of Automata in the Prisoners' Dilemma”, Journal of Economic Behaviour and Organization, Vol. 43, pp. 239-262 .

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Financial support from the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303 at the University of Bonn is gratefully acknowledged. I thank George Mailath, Georg Nöldeke, Karl Schlag, Avner Shaked, Bryan Routledge and several participants of Seminars in Bonn, Florence, Jerusalem, Maastricht, and Tel Aviv for comments.