Philip LaPorte

Summary

In a repeated game, reactive strategies decide the next move based on the opponent’s previous move. The donation game is a simple cooperative dilemma. It has two actions—‘cooperate’ and ‘defect’—and one parameter—the cost-to-benefit ratio of cooperation, \(c\). We define an evolutionary process on the ‘positive’ reactive strategies. We prove that cooperation is more abundant than defection when \(c<1-1/\sqrt{2}\approx 0.29\). This value has a geometric interpretation and is independent of two ‘noise’ parameters which define the process.