Cooperation and Local Interactions in the Prisoners ’ Dilemma Game

* I want to thank Hans Haller and Mark Stegeman for their valuable suggestions and support. The paper benefited from the comments of participants in the 1997 SITE Summer Workshop. Abstract We consider a population of players playing a Prisoners' Dilemma Game in a local interaction setting, using a formalism of automata networks. Sufficient conditions for existence of an equilibrium where cooperation coexists with non-cooperation (a mixed equilibrium) are derived and properties of an equilibrium are discussed. In a mixed equilibrium the highest payoff will be obtained by a cooperator. For a special one-dimensional case the equilibrium set is fully characterized. We further consider a model where agents can choose (to some extent) whom of their neighbors they want to play with. Results of computer simulations are reported. The most striking feature of simulations is the fact that very organized structures can be observed starting with completely random initial conditions.