Computer Science Department
School of Computer Science, Carnegie Mellon University


An Evolutionary Resolution to the Finitely
Repeated Prisoner's Dilemma Paradox

Daniel B. Neill

June 2003

Keywords: Game theory, evolutionary games, Finitely Repeated Prisoner's Dilemma

Argument by backward induction forces us to conclude that two "rational" players will defect on every turn of the Finitely Repeated Prisoner's Dilemma (FRPD) game, thus performing significantly worse than agents with imperfect rationality. When this game is treated from an evolutionary perspective, using the standard evolutionary model, we encounter a similar paradox: a population which cooperates through turn k can be invaded by a strategy which cooperates through turn k-1, and this process continues until the population is dominated by defectors. However, though the strategy of continual defection is evolutionarily stable, it is inferior to nearly all other FRPD strategies: a bistable equilibrium occurs, in which a very small proportion of the other strategy can take over the population. Thus we propose and defend an alternative evolutionary model, a random invasion model in which "evolutionary dominance" is used instead of Maynard Smith's invasion criteria. This model combines the Lamarckian spread of ideas through a population with Darwinian natural selection of the organisms adopting those ideas, and thus is a more reasonable model of communicating populations. When the new evolutionary model is applied to the Finitely Repeated Prisoner's Dilemma, we find that defectors dominate the population for very short FRPD games, but as game length increases, it becomes more and more certain that successful strategies will cooperate until near the end of the game. Defining rationality based on evolutionary fitness (or fictitious evolutionary play) using this model, we achieve a resolution to the Finitely Repeated Prisoner's Dilemma paradox. Additionally, the model can be generalized and applied to many other decision situations, and thus it serves as a possible standard for rational decision-making under uncertainty.

21 pages

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