.
Résumé :
In the 70’s, Thomas Schelling [10, 11, 12] introduced several simple models in order to discuss the consequences, at the collective level, of social influence on individual choices. There is indeed a wide variety of situations where the choice of an individual depends on the one of others. The decision of leaving a neighbourhood, to attend a seminar, to go to a popular restaurant or to participate to a strike, are typical examples. For several Schelling’s models, which are simple to formulate but not that simple to analyze, links have been exhibited with physical systems, leading to various studies making use of tools taken from statistical physics. This is in particular the case of the segregation model [10,7,8,3], probably the most popular among Schelling’s models, often used by the agent-based-modelling community as a paradigm for the emergence of collective behaviour. Since this model has already been discussed in this working group on Interactions, I will not say much about it, except may be for shortly presenting some recent results [3] on the “phase diagram” (which gives, in the space of parameters, the regions with qualitatively different collective behaviours, and the nature of the transitions between them), and on links with the physics of materials made of two type of atoms and mobile vacancies, described by the “Blume-Imry-Griffiths model [2]”. I will discussed with more details Schelling’s “Dying seminar” [11], which allows to discuss the general case of binary choice with positive externalities and heterogeneous idiosyncratic preferences. This model has been shown to be formally equivalent to the Random Field Ising model (RFIM), making links with an important literature on the statistical physics of disordered (that is heterogeneous) systems (see e.g. [14]). Making use of a formulation which is convenient for both market and non market contexts, I will first consider the Nash equilibria, notably providing the typical “phase diagram” showing the genericity of multiple equilibria in such systems [4, 6, 9]. Then I will reconsider [5,6] Becker’s analysis [1] attributing to social interactions the fact that some popular restaurants do not increase their prices despite a persistent excess demand. If there is time, which is unlikely, I will present some results on the dynamics with learning agents [13] (convergence towards stationary states more or less close to the Nash equilibria).
Jean-Pierre Nadal (CNRS, EHESS, CAMS)