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

Optimal Joint Allocation of Efforts in Inclusive Fitness by Related Individuals