Multi-group binary choice with social interaction and a random communication structure—A random graph approach

Matthias Löwe, Kristina Schubert and Franck Vermet

Physica A: Statistical Mechanics and its Applications, 2020, vol. 556, issue C

Abstract: We construct and analyze a random graph model for discrete choice with social interaction and several groups of equal size. We concentrate on the case of two groups of equal sizes and we allow the interaction strength within a group to differ from the interaction strength between the two groups. Given that the resulting graph is sufficiently dense we show that, with probability 1, the average decision in each of the two groups is the same as in the fully connected model. In particular, we show that there is a phase transition: If the interaction among a group and between the groups is strong enough the average decision per group will either be positive or negative and the decision of the two groups will be correlated. We also compute the free energy per particle in our model.

Keywords: Ising model; Curie–Weiss model; Equilibrium statistical mechanics; Block model; Graphical models; Random graphs; Social interaction; Large deviations (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120303678

DOI: 10.1016/j.physa.2020.124735

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