title: Utility rate equations of group population dynamics in biological and social systems.
abstract: We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.
authors.affiliation: Department of Management, Technology and Economics, ETH Zürich, Swiss Federal Institute of Technology, Zürich, Switzerland ; Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia.
authors.forename: Vyacheslav I
authors.initials: VI
authors.lastname: Yukalov
authors.affiliation: Department of Management, Technology and Economics, ETH Zürich, Swiss Federal Institute of Technology, Zürich, Switzerland ; Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia.
authors.forename: Elizaveta P
authors.initials: EP
authors.lastname: Yukalova
authors.affiliation: Department of Management, Technology and Economics, ETH Zürich, Swiss Federal Institute of Technology, Zürich, Switzerland ; Swiss Finance Institute, c/o University of Geneva, Geneva, Switzerland.
authors.forename: Didier
authors.initials: D
authors.lastname: Sornette
mesh_terms: D000818:Animals; D001516:Bees / Q000502:physiology; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical; D011157:Population Dynamics; D012919:Social Behavior; D013598:Systems Theory