I will present a work which shows how tools coming from physics can be used to work on social models.
This research originates with a work on Schelling's segregation model. This toy model shows how spatial segregation can happen in a city even if agents do not really desire it. The introduction of a potential function reflecting individual welfare allowed us to solve analytically a version of this famous model (S. Grauwin, E. Bertin, R. Lemoy, P. Jensen, PNAS 2009). This same framework, used in an inhomogeneous space, shows that utility or welfare in socio-economic models corresponds to a chemical potential in physics (R. Lemoy, E. Bertin, P. Jensen, EPL 2011).
I will mainly speak about a more recent work, where the urban rental housing market is studied with a simple price formation model. Minimal interactions between tenants and landlords yield price dispersion, in a model which is very parsimonious compared to works of the economic literature. Indeed, agents have very limited information and a probabilistic behavior, which departs from the standard “optimizing agent” framework. This model is studied with simulations, and approximated analytically using a biased randow walk (R. Lemoy, E. Bertin, to appear in JSTAT).
R. Lemoy, E. Bertin, to appear in JSTAT http://arxiv.org/abs/1203.5298
R. Lemoy, E. Bertin, P. Jensen, EPL 2011
S. Grauwin, E. Bertin, R. Lemoy, P. Jensen, PNAS 2009