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.
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- Zizzo, D.J. & Oswald, A., 2000.
"Are People Willing to Pay to Reduce Others' Incomes?,"
The Warwick Economics Research Paper Series (TWERPS)
568, University of Warwick, Department of Economics.
- Daniel J. ZIZZO & Andrew J. OSWALD, 2001. "Are People Willing to Pay to Reduce Others'Incomes?," Annales d'Economie et de Statistique, ENSAE, issue 63-64, pages 39-65.
- Clark, Andrew E. & Oswald, Andrew J., 1998. "Comparison-concave utility and following behaviour in social and economic settings," Journal of Public Economics, Elsevier, vol. 70(1), pages 133-155, October.
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