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Reilly’s Law and Logistic Type Equation in a Model for Studying Group Selection and Intercity Relations


This paper presents a model based on logistic type equations, but taking Reilly’s Law into account. It consists of differential equations, each of which describes the dynamics of a population located at the center of a territory whose resources it exploits. Similar differential equations, but without elements that take into account the Reilly’s Law, have already been presented for studying the evolution of altruism from binary altruism (between two individuals) to Benthamian altruism (toward the group).  The model presented here aims to study the outcome of competition for resources at least partially shared by populations concentrated at different points. It shows that a group’s degree of cohesion is crucial to its survival if it competes with other groups for resources, even without the use of violence. It also shows that cooperation can replace competition between different populations with mutual benefits (even if the resulting equilibrium can be rather precarious). Finally, the differential equations used, while containing elements similar to those found in Newton’s gravitational law (as well as Reilly’s), predict the existence, alongside the force of attraction between economic actors, of its opposite (that is a sort of social antigravity).


Keywords: Logistic-Reilly hybrid model, altruism and selfishness, benthamian altruism, group selection, synergies and social antigravity

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