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Statistical thermodynamics for choice models on graphs

Author

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  • Majka, Arkadiusz
  • Wiślicki, Wojciech

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.

Suggested Citation

  • Majka, Arkadiusz & Wiślicki, Wojciech, 2004. "Statistical thermodynamics for choice models on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 645-663.
    • Handle: RePEc:eee:phsmap:v:337:y:2004:i:3:p:645-663
    DOI: 10.1016/j.physa.2004.01.063
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    Citations

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    Cited by:

    1. Ted Theodosopoulos, 2004. "Uncertainty relations in models of market microstructure," Papers math/0409076, arXiv.org, revised Feb 2005.
    2. Theodosopoulos, Ted & Yuen, Ming, 2007. "Properties of the wealth process in a market microstructure model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 443-452.
    3. Ted Theodosopoulos & Ming Yuen, 2006. "Imbalance attractors for a strategic model of market microstructure," Papers math/0605421, arXiv.org.
    4. Theodosopoulos, Ted, 2005. "Uncertainty relations in models of market microstructure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 209-216.

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