Discrete Choices under Social Influence, Generic Properties

Mirta Gordon, Jean-Pierre Nadal (), Denis Phan () and Viktoriya Semeshenko
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Mirta Gordon: AMA - Analyse de données, Modélisation et Apprentissage automatique [Grenoble] - LIG - Laboratoire d'Informatique de Grenoble - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - INPG - Institut National Polytechnique de Grenoble - CNRS - Centre National de la Recherche Scientifique
Jean-Pierre Nadal: CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, LPS - Laboratoire de Physique Statistique de l'ENS - FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Viktoriya Semeshenko: Departamento de Economía [Buenos Aires] - Facultad de Ciencias Económicas [Buenos Aires] - UBA - Universidad de Buenos Aires [Buenos Aires]

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Abstract: We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. However, even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non-monotonic. Thus, depending on the price, there are either one or several equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited. We also discuss the links between the model and the random field Ising model studied in the physics literature.

Keywords: Discrete choice; random field Ising models; random utility models; collective phenomena; heterogeneous agents; externalities; social influence (search for similar items in EconPapers)
Date: 2012-04-26
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Published in Mathematical Models and Methods in Applied Sciences, 2012, 19 (supp01), pp.1441-1481. ⟨10.1142/S0218202509003887⟩

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Related works:
Working Paper: Discrete Choices under Social Influence: Generic Properties (2012)
Working Paper: Discrete Choices under Social Influence:Generic Properties (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-04004539

DOI: 10.1142/S0218202509003887

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