COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 937

"Aggregation and Imperfect Competition: On the Existence of Equilibrium"

Andrew Caplin and Barry Nalebuff

February 1990

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 characteristic approach, and probabilistic choice together in a unified framework.

To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces these theorems and develops the application to super-majority voting rules.

Keywords: Imperfect competition, Bertrand equilibrium, differentiated products, prices, price competition

JEL Classification: 611, 022, 511