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Equilibria in Logit Models of Social Interaction and Quantal Response Equilibrium

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The Quantal Response Equilibrium (QRE) extends the notion of Nash equilibrium in game theory to a corresponding stochastic equilibrium model. In QRE models, perfectly rational expectations equilibrium embodied in mixed strategy Nash equilibrium is replaced by an imperfect, or noisy, rational expectations equilibrium. An important subclass of QRE is the logit models of social interaction. It is known that at least one equilibrium exists in QRE models, but it is not known if, and when, there exist several equilibria. In this paper we discuss cases when unique- or several equilibria exist in two-persons multinomial logit QRE models. Second, we consider the equilibria in multinomial models with social interaction. Third, we discuss corresponding dynamic games and stability. Finally, we consider several examples.

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  • Dagsvik, John K., 2020. "Equilibria in Logit Models of Social Interaction and Quantal Response Equilibrium," HERO Online Working Paper Series 2020:5, University of Oslo, Health Economics Research Programme, revised 09 Mar 2023.
    • Handle: RePEc:hhs:oslohe:2020_005
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    File URL: https://www.med.uio.no/helsam/forskning/nettverk/hero/publikasjoner/skriftserie/2023/2023-1.pdf
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    Cited by:

    1. Ge, Ge & Godager, Geir, 2021. "Predicting strategic medical choices: An application of a quantal response equilibrium choice model," Journal of choice modelling, Elsevier, vol. 39(C).

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    More about this item

    Keywords

    Stochastic game theory; Logit QRE; Logit models with social interaction; Multiple equilibria;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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