The Evolutionary Stability of Cooperation

Is cooperation without central authority stable? If so, how robust is it? Despite what might be the conventional wisdom, The Evolution of Cooperation did not solve this problem deductively. In fact, results obtained later by others seem to have contradicted the book's main message. Reexamining this exceptionally influential work yields a new picture. Part of Axelrod's evolutionary story turns out to be false. But the main intuition, that retaliatory strategies of conditional cooperation are somehow advantaged, proves correct in one specific and significant sense: Under a standard evolutionary dynamic these strategies require the minimal frequency to stabilize. Hence, they support the most robust evolutionary equilibrium: the easiest to reach and retain. Moreover, the less efficient a strategy, the larger is its minimal stabilizing frequency; Hobbesian strategies of pure defection are the least robust. Our main theorems hold for a large class of games that pose diverse cooperation problems: prisoner's dilemma, chicken, stag hunt, and many others.