Selfish Altruism, Fierce Cooperation and the Emergence of Cooperative Equilibria from Passing and Shooting

There is continuing debate about what explains cooperation and self-sacrifice in nature and in particular in humans. This paper suggests a new way to think about this famous problem. I argue that, for an evolutionary biologist as well as a quantitative social scientist, the triangle of two players in the presence of a predator (passing and shooting in 2-on-1 situations) is a fundamental conceptual building-block for understanding these phenomena. I show how, in the presence of a predator, cooperative equilibria rationally emerge among entirely selfish agents. If we examine the dynamics of such a model, and bias the lead player (ball possessor with pass/shoot i.e. cooperate/defect dilemma) in the selfish direction by only an infinitesimal amount, then, remarkably, the trajectories of the new system move towards a cooperative equilibrium. I argue that predators are common in the biological jungle but also in everyday human settings. Intuitively, this paper builds on the simple idea - a familiar one to a biologist observing the natural world but perhaps less so to social scientists - that everybody has enemies. As a technical contribution, I solve these models analytically in the unbiased case and numerically by an O(h5) approximation with the Runge-Kutta method.