Abstract
This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
Zusammenfassung
In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß — angenommen Nash Gleichgewichte existieren — diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson S (1987) Spatial competition and price leadership. International Journal of Industrial Organization 5: 369–398
Bauer A, Domschke W, Pesch E (1993) Competitive location on a network. European Journal of Operational Research 66: 372–391
Eiselt HA (1992) Hotelling's duopoly on a tree. Annals of Operations Research 40:195–207
Eiselt HA, Laporte G (1991) Locational equilibrium of two facilities on a tree. Operations Research/Recherche opérationnelle 25: 5–18
Eiselt HA, Laporte G, Thisse J-F (1993) Competitive location models: a framework and bibliography. Transportation Science 27: 44–54
Friesz TL, Miller TC, Tobin RL (1988) Competitive network location models: a survey. Papers of the Regional Science Association 65: 47–57
Goldman AJ (1971) Optimal center location in simple networks. Transportation Science 5: 212–221
Hakimi SL (1983) On locating new facilities in a competitive environment. European Journal of Operational Research 12: 29–35
Hakimi SL (1990) Locations with spatial interactions: competitive locations and games. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley Interscience, New York, pp 439–478
Hotelling H (1929) Stability in competition. Economic Journal 39: 41–57
Katz IN, Cooper L (1981) Facility location in the presence of forbidden regions. 1. Formulation and the case of Euclidean distances with one forbidden circle. European Journal of Operational Research 6: 166–173
Labbé M, Hakimi SL (1991) Market and locational equilibrium for two competitors. Operations Research 39: 749–756
ReVelle C (1986) The maximum capture or ‘sphere of influence’ location problem: Hotelling revisited on a network. Journal of Regional Science 26: 343–358
Stackelberg H von (1943) Grundlagen der theoretischen Volkswirtschaftslehre. Translated by: Peacock AT, The Theory of the Market Economy (1952). Hodge, London Edinburgh Glasgow
Tirole J (1995) The theory of industrial organization. The MIT Press, Cambridge, MA
Tovey CA (1993) Dynamical convergence of majority rules toε-cores in Euclidean spaces. Working paper, School of Industrial and Systems Engineering, Georgia Tech, Atlanta, GA
Wendell RE, McKelvey RD (1981) New perspectives in competitive location theory. European Journal of Operational Research 6: 174–182
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eiselt, H.A., Bhadury, J. Reachability of locational Nash equilibria. OR Spektrum 20, 101–107 (1998). https://doi.org/10.1007/BF01539861
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01539861