Reactive Strategies: The Establishment of Cooperation

TL;DR

This paper investigates how the success of cooperative strategies like Generous-tit-for-tat depends on the number of available strategies and the version of the replicator dynamics used, revealing conditions under which defection prevails.

Contribution

It demonstrates that the dominance of Generous-tit-for-tat is contingent on the number of strategies and the replicator model, challenging previous assumptions.

Findings

Generous-tit-for-tat wins with few strategies

Defection dominates as the number of strategies increases

The replicator model version influences strategy success

Abstract

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.