Multinomial Logit Market Share Models: Equilibrium Characteristics and Strategic Implications

Abstract

We specify and analyze the conditions under which the MNL market share models are appropriate for equilibrium analysis. Our results show that a linear price response function as is often used in empirical research, in conjunction with the typical concavity assumed in a large range of marketing response functions, would yield an interior equilibrium solution. We then consider the optimal reactions on pricing and marketing spending to entry and potential market expansion. In the context of the MNL models, we demonstrate that the entry of a new brand evokes a decrease in the equilibrium prices of the existing brands as a defensive reaction. This is true in both an expanding market as well as a fixed market. However, while new entry into a fixed market would trigger the incumbents to lower the marketing expenditure, we show that firms tend to raise marketing activities as they experience market expansion. Consequently, there exist distinct possibilities that marketing efforts for the existing brands increase in view of entry in an expanding market. Further managerial and marketing implications for endogeneity of the number of firms are explored.

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