## Is Cooperation Ever an Evolutionary Stable Strategy?

In last Friday’s lecture discussing the concept of evolutionary game theory, I was struck when professor Easley presented the game in which aggressive strategy prevailed over the passive strategy. More specifically, I was quite incredulous that in this example aggressive behavior was an evolutionary stable strategy while passive was not, when in reality there are many examples of real-world animals (humans included) that exist through cooperative social structures. As such, I went to searching for articles and scholarly papers that explored the concept of cooperative, evolutionary stable strategies, and landed upon this article. This article presents an account of the modern developments in the field of evolutionary game theory, and centers around three scholars: Press and Dyson, who published a paper finding that extortion (or uncooperative behavior) was the only evolutionary stable strategy; and Plotkin, a University of Pennsylvania evolutionary biologist that was similarly skeptical of these results. Building upon Press and Dyson’s work, Plotkin was able to create an evolutionary game theory model that mathematically substantiated the claim that cooperative behavior can be an evolutionary stable strategy, but even these results were far from equivocal.

To begin with the building block to Plotkin’s findings, Press and Dyson centered their argument against the possibility of cooperative behavior on an evolutionary game in which one player employed a strategy of extortion. In this game, the player that extorted the other player basically defected to selfish strategies with a probability that made it so that the non-extortion player would try to cooperate in order to incentivize the defector to cooperate back, thus yielding the social-welfare maximizing equilibrium. Through this framework, Press and Dyson found that as long as the extortionist cooperated just enough to incite his opponent to employ this desperate, cooperative behavior as described above, the extortionist would always end the game with the higher payoff. While Plotkin was intrigued by this game and impressed by its mathematical elegance, he was unconvinced and decided to examine whether a cooperative would ever prevail. Much to his delight, Plotkin found a strategy, which he dubbed generosity, that yielded a higher payoff compared to the extortion strategy when tested in a game involving a high number of other players. The generosity strategy, whereby a player would always cooperate when his opponent does and would only defect at a certain probability when his opponent would defect, consistently prevailed over the extortion strategy in an evolutionarily realistic game involving more than simply two players. However, Plotkin did find that this generosity strategy was fragile over time, and if a population hit a breaking point whereby enough players became extortionists, the population would revert to a dominant, aggressive set of strategies. Thus, this body of work combines to produce a variety of contradictory conclusions, which emphasizes the reality that while evolutionary game theory can sometimes model real-life behavior, academic expectations of this network theory must be tempered by the fact that even slight changes to the model can produce contradictory results.