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Location Equilibria Under Alternative Solution Concepts

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  • Simon P. Anderson

Abstract

We provide a comparison of the location equilibria in a duopoly model under three alternative solution concepts. The first one is a simultaneous price and location game, the second is a two-stage location-then-price game. Third, we introduce a new solution concept, a two-stage price-then-location game. It is well known that no (pure strategy) equilibrium usually exists under the first two solution concepts when products are homogenous. We show this is also true for the third concept. However, introducing sufficient product heterogeneity in a specific manner restores the existence of equilibrium in each case. We argue that, under certain "regularity" conditions, equilibrium locations are farther apart under the location-then-price game than in the simultaneous game. We provide simulation results for a specific functional form (the logit model) which illustrates this result, and show that locations in the price-then-location game may be either closer or farther from the center than simultaneous game. Another contribution of the paper is to introduce a no-purchase option into the logit model of spatial competition.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 885.

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Date of creation: Nov 1989
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Handle: RePEc:nwu:cmsems:885

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Jonathan H Hamilton & James F. Klein & Eytan Sheshinski & Steven M. Slutsky, 1994. "Quantity Competition in a Spatial Model," Canadian Journal of Economics, Canadian Economics Association, vol. 27(4), pages 903-17, November.
  2. ANDERSON, S.P. & de PALMA, A. & THISSE, J.-F., 1987. "Spatial price policies and duopoly," CORE Discussion Papers 1987037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Anderson, S., 1986. "Equilibrium existence in the linear model of spatial competition," CORE Discussion Papers 1986013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. David J. Salant, 1986. "Equilibrium in a Spatial Model of Imperfect Competition with Sequential Choice of Locations and Quantities," Canadian Journal of Economics, Canadian Economics Association, vol. 19(4), pages 685-715, November.
  5. Eaton, B Curtis & Lipsey, Richard G, 1978. "Freedom of Entry and the Existence of Pure Profit," Economic Journal, Royal Economic Society, vol. 88(351), pages 455-69, September.
  6. Anderson, Simon P & de Palma, Andre, 1988. "Spatial Price Discrimination with Heterogeneous Products," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 573-92, October.
  7. Novshek, William, 1980. "Equilibrium in simple spatial (or differentiated product) models," Journal of Economic Theory, Elsevier, vol. 22(2), pages 313-326, April.
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