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.

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相关个人在包容性健身中的最佳联合分配

家庭是亲情和合作的场所，也是冲突的场所。在他著名的论文“亲代冲突”中，罗伯特·L·特里弗斯 (Robert L. Trivers) 以 WD Hamilton 的包容性适合的概念为基础来论证亲子关系中的遗传冲突，并得出对冲突强度的数值预测。我们提出了一个博弈论的数学模型，它描述了一个家庭的每个成员如何分配她的资源预算以最大化她的包容性；后者由个人适应度之和加上由赖特关系系数加权的亲属适应度之和组成。我们将最优分配配置文件定义为纳什均衡，并根据资源预算、关系系数和个人适应度的导数来表征解决方案。