Statistical thermodynamics for choice models on graphs

Abstract

Formalism based on equilibrium statistical thermodynamics is applied to communication networks of decision-making individuals. It is shown that in statistical ensembles for choice models, properly defined disutility plays the same role as energy in statistical mechanics. We demonstrate additivity and extensivity of disutility and build three types of equilibrium statistical ensembles: the canonical, the grand canonical and the super-canonical. Using Boltzmann probability measure one can reproduce the logit choice model. We propose using q-distributions for temperature evolution of moments of stochastic variables. The formalism is applied to networks with fixed topologies of different degrees of symmetry, for which analytic and numerical results are presented.