Scandinavian Working Papers in Economics

HERO Online Working Paper Series,
University of Oslo, Health Economics Research Programme

No 2020:5: Equilibria in Logit Models of Social Interaction and Quantal Response Equilibrium

John K. Dagsvik ()
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John K. Dagsvik: Department of Health Management and Health Economics, Postal: HERO / Department of Health Management and Health Economics, P.O. Box 1089 Blindern, NO-0317 Oslo, Norway

Abstract: 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.

Keywords: Stochastic game theory; Logit QRE; Logit models with social interaction; Multiple equilibria

JEL-codes: C02; C25; C62; C72; C73

Language: English

28 pages, First version: October 6, 2020. Revised: March 9, 2023. Earlier revisions: March 9, 2023.

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