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.
Caplin, Andrew S. and Nalebuff, Barry, "Aggregation and Imperfect Competition: On the Existence of Equilibrium" (1990). Cowles Foundation Discussion Papers. 1180.