Abstract
The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of conditional probabilities that represent the response of decision pathways given previous plays. We find that if these stochastic strategies are encoded as genes that undergo Darwinian evolution, the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory, which could be either cooperation or defection. A transition between cooperative and defective attractors occurs as a function of different parameters such as mutation rate, replacement rate, and memory, all of which affect a player's ability to predict an opponent's behavior. These results imply that in populations of players that can use previous decisions to plan future ones, cooperation depends critically on whether the players can rely on facing the same strategies that they have adapted to. Defection, on the other hand, is the optimal adaptive response in environments that change so quickly that the information gathered from previous plays cannot usefully be integrated for a response.
Highlights
The evolution of cooperation is difficult to understand within Darwinian theory [1,2,3]
The observed cooperation between genes, cells, tissues, and higher organisms represents a paradox for Darwinian evolution, because the individual success of cheating is rewarded before its long-term detrimental consequences are felt
The tension between cooperation and defection can be represented by a simple game, which has been used to study the conflicts between decisions to cooperate or defect
Summary
The evolution of cooperation is difficult to understand within Darwinian theory [1,2,3]. Previous work has shown that cooperation can only emerge in the presence of different enabling mechanisms. The main ones are direct reciprocity [6,10] (which can emerge when players play against each other repeatedly), spatial reciprocity [7], which is ensured if players only play neighbors on a regular grid (or more generally, on arbitrary graphs, giving rise to ‘‘network reciprocity’’ [11]), tag-based selection [12] (where players can recognize each other using some observable trait), kin selection [13], indirect reciprocity [14,15] (where cooperative or altruistic acts increase a player’s reputation), or group selection [16]. The co-evolution of strategies with the different enabling mechanisms can increase cooperation [21]. In all the discussed scenarios, a player’s strategy is such that they either cooperate or defect in a deterministic manner, sometimes conditionally on previous plays
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