Reactive Strategies: The Establishment of Cooperation

Cooperation is usually represented as a Prisoner's Dilemma game. Although individual self-interest may not favour cooperation, cooperation can evolve if, for example, players interact multiple times adjusting their behaviour accordingly to opponent's previous action. To analyze population dynamics, replicator equation has been widely used under several versions. Although it is usually stated that a strategy called Generous-tit-for-tat is the winner within the reactive strategies set, here we show that this result depends on replicator's version and on the number of available strategies, stemming from the fact that a dynamics system is also defined by the number of available strategies and not only by the model version. Using computer simulations and analytical arguments, we show that Generous-tit-for-tat victory is found only if the number of strategies available is not too large, with defection winning otherwise.