Utility Rate Equations of Group Population Dynamics in Biological and Social Systems

Vyacheslav I. Yukalov, E.P. Yukalova and Didier Sornette
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Vyacheslav I. Yukalov: Joint Institute for Nuclear Research and ETH Zurich
E.P. Yukalova: Joint Institute for Nuclear Research
Didier Sornette: Swiss Finance Institute and ETH Zürich

No 12-39, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 $10\%$ 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.

Keywords: trait groups; cooperators; defectors; regulators; evolution equations; evolutionally stable strategies; self-organized societies (search for similar items in EconPapers)
JEL-codes: C30 C79 H59 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2012-12
New Economics Papers: this item is included in nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1239

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