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Nowak and May's Prisoner's Dilemma

In a 1992 Nature article, Nowak & May published surprising findings in their spatial model of the Prisoner’s Dilemma. Although the Nash equilibrium of the standard Prisoner’s Dilemma is for neither player to cooperate, in Nowak & May’s model, cooperation and defection dynamically coexist, spreading and receding across the 2-dimensional lattice of ‘players.’ Each player considers the payoffs that each of its neighbors receives by playing their current strategy (cooperate or defect), and then changes their strategy to the highest-scoring strategy among their neighbors. Defecting (colored in red, with first-time defectors yellow) spreads from a single initial defector at the center, but cooperating (blue, with first-time cooperators green) is always able to remain a significant strategy.

A year after the publishing of Nowak & May’s model, Huberman & Glance responded in PNAS, proving that the hypnotizing dynamic patterns created by the Nowak & May model were an artifact of synchronous updating across all players — if players update asynchronously, defecting will become the dominant equilibrium strategy.