"Socio-Dynamic Discrete Choice: Analytical Results for the Nested Logit Model"
Suppose you have the possibility to choose to adopt one of a number of discrete behaviors or to choose to buy one of a number of different products. Moreover, suppose the choice is multi-dimensional or more generally, that there are common unobserved attributes of the choice alternatives. A classic approach to statistical prediction in such a situation given an observed sample of decision-making agents in a population is the nested logit model, pioneered by Ben-Akiva (1973). Now suppose your choice to adopt a discrete behavior or buy a discrete product is influenced by what choices your neighbors and/or members of your social network make, or by your personal general perception of percentages of segments of the population making these choices. Brock and Durlauf (2003) have proposed a variant of the nested logit model for handling multi-dimensional choice of group and behavior, noting that, “There has yet to be any analysis of (such) models... when self-consistency is imposed on the expected group choice percentages. Such an analysis should provide a number of interesting results.” It is my aim to fill this gap. I present benchmark analytical results for mean-field, steady-state corner solutions in parameter space derived drawing on techniques from the mathematics of dynamical systems and bifurcation theory. I also show that the nested logit model reduces to the well-known Potts model in statistical mechanics under various simplifying assumptions. I conclude highlighting limitations of the present study and my recommendations for future work.