Siegfried, Tom. "4 Smith’s Strategies--Evolution, altruism, and cooperation." A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature. Washington, DC: The National Academies Press, 2006.
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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
cooperation in a society. A reputation as a tit-for-tat player will induce opponents to cooperate with you, knowing that if they do, you will. And if they don’t, you won’t.
Alas, the story gets even more complicated. Just because tit for tat won Axelrod’s tournament, that doesn’t mean it’s the best strategy in the real world. For one thing, it rarely won in head-to-head competition against any other strategy; it just did the best overall (because strategies that defeated tit for tat often lost badly against other strategies).
In his talk at the conference, Nowak explored some of the nuances of the tit-for-tat strategy in a broader context. At first glance, tit for tat’s success seems to defy the Nash equilibrium implication that everyone’s best strategy is to always defect. The mathematics of evolutionary game theory, based on analyzing an infinitely large population, seems to confirm that expectation. However, Nowak pointed out, for a more realistic finite population, you can show that a tit-for-tat strategy, under certain circumstances, can successfully invade the all-defect population.
But if you keep calculating what would happen if the game continues, it gets still more complicated. Tit for tat is an unforgiving strategy—if your opponent meant to cooperate but accidentally defected, you would then start defecting and cooperation would diminish. If you work out what would happen in such a game, the tit-for-tat strategy becomes less successful than a modified strategy called “generous tit for tat.” So a generous tit-for-tat strategy would take over the population.
“Generous tit for tat is a strategy that starts with cooperation, and I cooperate whenever you cooperate, but sometimes I will cooperate even when you defect,” Nowak explained. “This allows me to correct for mistakes—if it’s an accidental mistake, you can correct for it.”16
As the games go on, the situation gets even more surprising, Nowak said. The generous tit-for-tat approach gets replaced by a strategy of full-scale cooperation! “Because if everybody plays generous tit for tat, or tit for tat, then nobody deliberately tries to defect; everybody is a cooperator.” Oh Happy Days.