Statistical thermodynamics for choice models on graphs

TL;DR

This paper applies statistical thermodynamics principles to choice models on graphs, linking disutility to energy, and develops ensembles to analyze decision-making networks with potential applications in airline and economic decision support.

Contribution

It introduces a thermodynamic formalism for choice models on graphs, including new ensembles and the use of q-distributions for modeling temperature evolution.

Findings

Reproduces the logit choice model using Boltzmann-like probabilities.

Derives analytical results for different network topologies.

Demonstrates the model's applicability to airline networks and economic decisions.

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 can play 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-like probability measure one reproduce the logit choice model. We also propose using q-distributions for temperature evolution of moments of stochastic variables. The formalism is applied to three network topologies of different degrees of symmetry, for which in many cases analytic results are obtained and numerical simulations are performed for all of them. Possible applications of the model to airline networks and its usefulness for practical support of economic decisions is pointed out.