Optimal Joint Allocation of Efforts in Inclusive Fitness by Related Individuals

Abstract: Families are places of affection and cooperation, but also of conflict. In his famous paper Parent-Offspring Conflict, Robert L. Trivers builds upon W. D. Hamilton's concept of inclusive fitness to argue for genetic conflict in parent-offspring relationships, and to derive numerical predictions on the intensity of the conflict. We propose a mathematical model of game theory that depicts how each member of a family allocates her resource budget to maximize her inclusive fitness; this latter is made of the sum of personal fitness plus the sum of relatives fitnesses weighted by Wright's coefficients of relationship. We define an optimal allocation profile as a Nash equilibrium, and we characterize the solutions in function of resource budgets, coefficients of relationship and derivatives of personal fitnesses.