This paper considers Hotelling's duopoly model on a tree. It is shown that if both competitors have price and location as decision variables, no equilibrium exists. If prices are fixed in advance by the competitors, equilibria may exist. Conditions for this case are developed. Then the related sequential location problem is investigated. It is shown that it is usually beneficial for a facility not to locate first but to react to its competitor's location choice.
KeywordsNash Equilibrium Market Share Facility Location Profit Function Market Area
Unable to display preview. Download preview PDF.
- J. Bertrand, Théorie mathématique de la richesse sociale, Journal des Savants 48(1883)499–508.Google Scholar
- H.A. Eiselt, Different pricing policies in Hotelling's duopoly model, Cahiers C.E.R.O. (1992), forthcoming.Google Scholar
- H.A. Eiselt and G. Laporte, Locational equilibrium of two facilities on a tree, Oper. Res./recherche operationnelle 25(1991)5–18.Google Scholar
- H.A. Eiselt, G. Laporte and J.-F. Thisse, Competitive location models: A framework and bibliography, Transp. Sci. (1992), forthcoming.Google Scholar
- J.M. Enelow and J.M. Hinich,The Spatial Theory of Voting (Cambridge University Press, Cambridge, UK, 1984).Google Scholar
- A. Ghosh and B. Buchanan, Multiple outlets in a duopoly: A first entry paradox, Geograph. Anal. 20(1988)111–121.Google Scholar
- P. Hansen, M. Labbé, D. Peeters and J.-F. Thisse, Single facility location on networks, Ann. Discr. Math. 31(1987).Google Scholar
- E.C. Prescott and M. Visscher, Sequential location among firms with foresight, Rand J. Econ. 8(1977)378–393.Google Scholar