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- Title
Non-existence of Equilibrium for the Two-dimensional Three-firms Location Problem.
- Authors
Shaked, A.
- Abstract
Given a distribution of customers and a location of κ firms in the plane, assume that each customer buys one unit from the nearest firm and that the revenue of a firm is proportional to the number of customers it has. Underlying these assumptions is the assumption that the customer bears the transport costs and that these are determined by a monotonic function of the distance. A location of κ firms is an equilibrium if no firm can change its location so as to increase its revenue while the other κ - 1 firms are kept fixed (Nash equilibrium). B. C. Eaton and R. G. Lipsey [1] conjecture that no such equilibrium exists for κ ≥ 3. This note proves that the conjecture is true for κ = 3, for a continuous and connected customer distribution.
- Subjects
ECONOMIC equilibrium; ECONOMICS; INDUSTRIAL location; DISTRIBUTION (Economic theory); SUPPLY &; demand; NATURAL rate of unemployment; BUSINESS enterprises; CONSUMERS
- Publication
Review of Economic Studies, 1975, Vol 42, Issue 1, p51
- ISSN
0034-6527
- Publication type
Article
- DOI
10.2307/2296818