Sainte-Foy-lès-Lyon, France
Sainte-Foy-lès-Lyon, France

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Lemoy R.,University of Lyon | Lemoy R.,IXXI Complex Systems Institute | Bertin E.,IXXI Complex Systems Institute | Bertin E.,University of Lyon | And 2 more authors.
EPL | Year: 2011

In statistical physics, the conservation of particle number results in the equalization of the chemical potential throughout a system at equilibrium. In contrast, the homogeneity of utility in socio-economic models is usually thought to rely on the competition between individuals, leading to Nash equilibrium. We show that both views can be reconciled by introducing a notion of chemical potential in a wide class of socio-economic models, and by relating it in a direct way to the equilibrium value of the utility. This approach also allows the dependence of utility across the system to be determined when agents take decisions in a probabilistic way. Numerical simulations of a urban economic model also suggest that our result is valid beyond the initially considered class of solvable models. Copyright © EPLA, 2011.

Lambert G.,Ecole Normale Superieure de Lyon | Chevereau G.,Ecole Normale Superieure de Lyon | Chevereau G.,IXXI Complex Systems Institute | Bertin E.,Ecole Normale Superieure de Lyon | Bertin E.,IXXI Complex Systems Institute
Journal of Statistical Mechanics: Theory and Experiment | Year: 2011

We consider a simple decision model in which a set of agents randomly choose one of two competing shops selling the same perishable products (typically food). The satisfaction of agents with respect to a given store is related to the freshness of the previously bought products. Agents select with a higher probability the store that they are most satisfied with. Studying the model from a statistical physics perspective, both through numerical simulations and mean-field analytical methods, we find a rich behaviour with continuous and discontinuous phase transitions between a symmetric phase where both stores maintain the same level of activity, and a phase with broken symmetry where one of the two shops attracts more customers than the other. © 2011 IOP Publishing Ltd ans SISSA.

Grauwin S.,University of Lyon | Grauwin S.,IXXI Complex Systems Institute | Hunt D.,University of Lyon | Hunt D.,IXXI Complex Systems Institute | And 4 more authors.
Advances in Complex Systems | Year: 2011

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. © 2011 World Scientific Publishing Company.

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