The prisoner’s dilemma without synchrony

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Abstract
There are many situations in which biological organisms cooperate despite obvious incentives to do otherwise. Such situations are commonly modelled by using a paradigm known as the prisoner's dilemma. In this way cooperative behaviour has previously been shown to emerge in a model population of strategies. If players can make probabilistic choices, taking into account their co-player's previous action, a strategy known as 'generous tit for tat' dominates the long-term behaviour of such a population. If they can also take into account their own previous action, a strategy of 'win stay, lose shift' dominates instead. These models assumed that participants make their decisions in synchrony, which seems improbable in many biological situations. Here we show that the timing of decisions is critical in determining which strategy emerges in the long run. If individuals make their decisions at different times, neither of the above strategies survives given the usual payoffs. In the former case, generous tit for tat succumbs to inveterate defectors, and in the latter a new strategy takes over. This 'firm but fair' strategy is retaliatory yet highly cooperative. In particular, continued exploitation of a sucker is no longer a successful behaviour.