The Rise of Reciprocal Altruism–a Theory Based on the Centipede Game with Trivers-Payoffs

Reciprocal altruism is a fact. There are many within-species and between-species examples of such strategic interaction. At the same time, reciprocal altruism would appear to be impossible. In deep evolutionary time, exceedingly small differences in costs will suffice to make the difference between life and death. Genotypes carrying extra costs will perish. How could individuals carrying extra altruistic costs survive? This study searches for the answer by looking at the mathematical features of the centipede game with what we call Trivers-payoffs. The notion refers to the reciprocally asymmetrical structure of costs and benefits between two players. There is an altruist individual X who gives significant benefits to another individual Z at a negligible cost to herself, getting similarly weighted favors back from Z. (1) When relative payoffs of the centipede game are defined as Trivers-payoffs, when the game is modeled in a finite population of players, and when strategies are depicted as genetically hard-wired operational instructions, the originally lone altruist mutation is capable of surviving and reproducing for quite some time, and (2) when the lone altruist mutation gets her first partner, changes in payoffs are dramatic. The altruist mutation begins to gain in payoffs and hence also in frequency.