Economics and social sciences
Analogy between thermodynamic equilibria and Nash equilibria
We propose a framework for non-cooperative non-atomic anonymous games with a continuum of players which exhibit strong scale separation. In such games, the agents evolve their strategy variables on a much faster time-scale than their social configuration variables. This framework allows the derivation of a model describing the slow evolution of the social configuration variables as a consequence of the very fast evolution of the strategy variables. This fast evolution drives the agents towards a local Nash equilibrium. The slow evolution model depends on parameters that are computed from these local Nash equilibria. This framework allows to draw a parallel between local thermodynamic equilibria in kinetic theory and Nash equilibria in game theory.
These models are applied to various kinds of contexts: crowds, models of social herding behavior and models for the evolution of the wealth distribution within a heterogeneous economic environment, in the case of conservative and non-conservative economies. Such games can be seen as approximations of mean-field games of Lasry & Lions through a model predictive control approach.