Multiproduct Firms and Discrete Choice Models of Demand: Existence and Uniqueness of the Bertrand-Nash Equilibrium

No 20-24, Economics Discussion / Working Papers from The University of Western Australia, Department of Economics

Abstract: This paper proves the existence and uniqueness of Bertrand-Nash equilibrium in oligopolies, where each firm may sell multiple substitutes of the same good. Bertrand competition emerges as a limit case when the number of products per firm increases if the consumers’ willingness to pay for products follow a sufficiently slim-tailed distribution. In opposition, the double exponential distribution is not slim enough, and firms conserve monopolistic power even for an arbitrarily large number of products per firm. Moreover, the double exponential distribution provides closed-form solutions that relate to discrete choice theory. First, a duality with representative consumers helps recover multinomial logit (MNL) demand functions and constant elasticity of substitution (CES) utility functions. Second, the game in which firms sequentially set the quality, then the price of their products, has a unique equilibrium.

Keywords: Multiproduct firms; Price competition; Oligopoly; Discrete choice; Product differentiation (search for similar items in EconPapers)
JEL-codes: D21 D43 L12 L13 (search for similar items in EconPapers)
Pages: 31
Date: 2020
New Economics Papers: this item is included in nep-com, nep-dcm, nep-gth, nep-ind, nep-mic, nep-ore and nep-upt
Note: MD5 = 59d12f727f2139d91d3882c35cb8433a
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