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Effective Free Energy For Individual Dynamics

Author

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  • SEBASTIAN GRAUWIN

    (Université de Lyon, Laboratoire de Physique, ENS Lyon and CNRS, 46 allée d'Italie, F-69007 Lyon, France;
    IXXI Complex Systems Institute, 5 rue du Vercors, F-69007 Lyon, France)

  • DOMINIC HUNT

    (Université de Lyon, Laboratoire de Physique, ENS Lyon and CNRS, 46 allée d'Italie, F-69007 Lyon, France;
    IXXI Complex Systems Institute, 5 rue du Vercors, F-69007 Lyon, France)

  • ERIC BERTIN

    (Université de Lyon, Laboratoire de Physique, ENS Lyon and CNRS, 46 allée d'Italie, F-69007 Lyon, France;
    IXXI Complex Systems Institute, 5 rue du Vercors, F-69007 Lyon, France)

  • PABLO JENSEN

    (Université de Lyon, Laboratoire de Physique, ENS Lyon and CNRS, 46 allée d'Italie, F-69007 Lyon, France;
    IXXI Complex Systems Institute, 5 rue du Vercors, F-69007 Lyon, France)

Abstract

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.

Suggested Citation

  • Sebastian Grauwin & Dominic Hunt & Eric Bertin & Pablo Jensen, 2011. "Effective Free Energy For Individual Dynamics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 529-536.
    • Handle: RePEc:wsi:acsxxx:v:14:y:2011:i:04:n:s0219525911003128
    DOI: 10.1142/S0219525911003128
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    References listed on IDEAS

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    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
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    Cited by:

    1. Szabó, György & Hódsági, Kristóf, 2016. "The role of mixed strategies in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 198-206.
    2. Vincent Boitier, 2014. "Unemployment Dispersion and City Configurations: Beyond the Bid Rent Theory," Working Papers hal-00999559, HAL.

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