Using Attraction Models for Competitive Optimization: Pitfalls to avoid and Conditions to Check

An important contribution to understanding competition has been the development of market share models based on the relative attractiveness of brands within a competitive set. These models have been used extensively as statistical tools to analyze and represent demand data. They have also been used for analytical studies of competitive optimization, but this entails a number of challenges for the researcher. Preliminary guidance on the use of attraction models for optimization is available when the competing firms make decisions about price alone. However, to be applied to a general marketing context, market share models with multiple marketing instruments need to be specified. Existing research has not considered either the robustness or suitability of market share models for optimization when each firm makes a costly marketing mix decision in addition to setting price. The authors highlight several problems that arise when specific forms of the attraction model are used for equilibrium analysis. The most important problem relates to whether solutions identified through numerical simulation are unique. The objective is to explain the origin of these problems and then propose a methodology that avoids them. The authors propose an approach based on the multinomial logit model that allows an attraction model to be used for competitive optimization. By placing a number of restrictions on the exogenous parameters, a unique solution is guaranteed.