Ingela Alger, and Jörgen W. Weibull, “A generalization of Hamilton’s rules – Love others how much?”, Journal of Theoretical Biology, vol. 299, April 2012, pp. 42–54.
According to [Hamilton, 1964a] and [Hamilton, 1964b] rule, a costly action will be undertaken if its fitness cost to the actor falls short of the discounted benefit to the recipient, where the discount factor is Wright's index of relatedness between the two. We propose a generalization of this rule, and show that if evolution operates at the level of behavior rules, rather than directly at the level of actions, evolution will select behavior rules that induce a degree of cooperation that may differ from that predicted by Hamilton's rule as applied to actions. In social dilemmas there will be less (more) cooperation than under Hamilton's rule if the actions are strategic substitutes (complements). Our approach is based on natural selection, defined in terms of personal (direct) fitness, and applies to a wide range of pairwise interactions.