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Letters to Nature
Nature 364, 56 - 58 (01 July 1993); doi:10.1038/364056a0

A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game

Martin Nowak* & Karl Sigmund

*Department of Zoology, University of Oxford, South Parks Road, Oxford 0X1 3PS, UK
Institut für Mathematik, Universit Wien, Strudlhofgasse 4, A-1090 Vienna, Austria

THE Prisoner's Dilemma is the leading metaphor for the evolution of cooperative behaviour in populations of selfish agents, especially since the well-known computer tournaments of Axelrod1 and their application to biological communities2,3. In Axelrod's simulations, the simple strategy tit-for-tat did outstandingly well and subsequently became the major paradigm for reciprocal altruism4 12. Here we present extended evolutionary simulations of heterogeneous ensembles of probabilistic strategies including mutation and selection, and report the unexpected success of another protagonist: Pavlov. This strategy is as simple as tit-for-tat and embodies the fundamental behavioural mechanism win-stay, lose-shift, which seems to be a widespread rule13. Pavlov's success is based on two important advantages over tit-for-tat: it can correct occasional mistakes and exploit unconditional cooperators. This second feature prevents Pavlov populations from being undermined by unconditional cooperators, which in turn invite defectors. Pavlov seems to be more robust than tit-for-tat, suggesting that cooperative behaviour in natural situations may often be based on win-stay, lose-shift.

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