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Multistability of impact, utility and threshold concepts of binary choice models

Author

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  • Ostasiewicz, K.
  • Tyc, M.H.
  • Radosz, A.
  • Magnuszewski, P.
  • Goliczewski, P.
  • Hetman, P.
  • Sendzimir, J.

Abstract

The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie–Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability.

Suggested Citation

  • Ostasiewicz, K. & Tyc, M.H. & Radosz, A. & Magnuszewski, P. & Goliczewski, P. & Hetman, P. & Sendzimir, J., 2008. "Multistability of impact, utility and threshold concepts of binary choice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(25), pages 6337-6352.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:25:p:6337-6352
    DOI: 10.1016/j.physa.2008.08.006
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    References listed on IDEAS

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    1. Brock, William A. & Durlauf, Steven N., 2001. "Interactions-based models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 54, pages 3297-3380, Elsevier.
    2. Arthur, W. Brian, 2006. "Out-of-Equilibrium Economics and Agent-Based Modeling," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 32, pages 1551-1564, Elsevier.
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    Cited by:

    1. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2016. "A family of models for Schelling binary choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 276-296.

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