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Discrete choice prox-functions on the simplex

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  • David Muller
  • Yurii Nesterov
  • Vladimir Shikhman

Abstract

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to natural probabilistic interpretations of the iteration steps. As illustration we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming naturally adjusts demand within a consumption cycle.

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  • David Muller & Yurii Nesterov & Vladimir Shikhman, 2019. "Discrete choice prox-functions on the simplex," Papers 1909.05591, arXiv.org.
    • Handle: RePEc:arx:papers:1909.05591
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    References listed on IDEAS

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    1. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    2. Small, Kenneth A, 1987. "A Discrete Choice Model for Ordered Alternatives," Econometrica, Econometric Society, vol. 55(2), pages 409-424, March.
    3. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    4. Kelvin J. Lancaster, 1966. "A New Approach to Consumer Theory," Journal of Political Economy, University of Chicago Press, vol. 74(2), pages 132-132.
    5. Fosgerau, Mogens & Melo, Emerson & Shum, Matt, 2017. "Discrete Choice and Rational Inattention: a General Equivalence Result�," MPRA Paper 76605, University Library of Munich, Germany.
    6. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
    7. Andriy Norets & Satoru Takahashi, 2013. "On the surjectivity of the mapping between utilities and choice probabilities," Quantitative Economics, Econometric Society, vol. 4(1), pages 149-155, March.
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    Cited by:

    1. Emerson Melo, 2021. "Learning in Random Utility Models Via Online Decision Problems," Papers 2112.10993, arXiv.org, revised Aug 2022.
    2. David Muller & Yurii Nesterov & Vladimir Shikhman, 2021. "Dynamic pricing under nested logit demand," Papers 2101.04486, arXiv.org.

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