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Aggregation and imperfect competition: On the existence of equilibrium. (English) Zbl 0738.90012
Summary: 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 A. Prékopa [Acta Sci. Math. 32, 301-316 (1971; Zbl 0235.90044)] and C. Borell [Period. Math. Hung. 6, 111-136 (1975; Zbl 0402.28007)]. Our companion paper [Econometrica 59, 1-23 (1991)] introduces these theorems and develops the application to super-majority voting rules.

MSC:
91B50 General equilibrium theory
91B24 Microeconomic theory (price theory and economic markets)
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