Aggregation and equilibrium with multinomial logit models

Abstract The problem of predicting the market share (or the usage) of a given product with disaggregate discrete choice models can be decomposed into two components: aggregation and equilibrium. The aggregation issue is rooted in the distribution of the choice model's explanatory variables across the population, while the equilibrium problem stems from the dependence of some of the explanatory variables on the alternatives' usage. This paper outlines the problem and suggests a mathematical programming formulation for it. This program is shown to have the same solution as the simultaneous aggregation/equilibrium problem, and thus solving the program also solves this problem. The paper also includes a description of an algorithm for minimizing the aggregation/equilibrium program and a simple example which illustrates the formulation and the algorithm. The focus of the paper is on multinomial logit models and on the area of travel demand, but the results are extended to a general class of random utility models and to other problems.