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Keywords:

  • evolution in complex systems;
  • evolutionary games;
  • Prisoners' Dilemma;
  • cellular automata

Abstract

Agents located on a 20 × 20 toroidal lattice play a Prisoners' Dilemma game with their Moore neighbors, adopting policies of cooperation and defection that depend only on their own action and the number of cooperators in the neighborhood in the last round of the game. These policies (“characters”) are encoded in 19-bit strings, which are subjected to evolution according to a genetic algorithm, with selection based on the cumulative scores of the agents in the neighborhood over 10 rounds of the basic game. Simulations examine the evolution of the population of characters over 1000 generations. Even with selection disabled, the genetic algorithm organizes the population into a small number of surviving characters clustered in spatially homogeneous regions. Selection for fitness rapidly achieves uniform cooperation. The characters evolved cooperate on the initial play, continue to cooperate when five or more of their neighbors cooperate, tend to defect defensively when they have cooperated and most of their neighbors have defected, and switch back to cooperation when five or more neighbors cooperate. When selection operates at the level of the whole society, however, the diversity of the population rapidly collapses, a single character predominates, and the cooperativeness of the dominating character is a matter of chance, so that there is no systematic tendency to evolve cooperation. © 2001 John Wiley & Sons, Inc.