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Journal Article

Aggregation and Imperfect Competition: On the Existence of Equilibrium

Andrew Caplin and Barry Nalebuff
Econometrica
Vol. 59, No. 1 (Jan., 1991), pp. 25-59
Published by: The Econometric Society
DOI: 10.2307/2938239
Stable URL: http://www.jstor.org/stable/2938239
Page Count: 35
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Aggregation and Imperfect Competition: On the Existence of Equilibrium
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Abstract

We present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions under which there exists a pure-strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristics approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prékopa (1971) and Borell (1975). Our companion paper (Caplin and Nalebuff (1991)) introduces these theorems and develops the application to super-majority voting rules.

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