Finding all pure strategy Nash equilibria in a planar location game
AbstractIn this paper, we deal with a planar location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served. We present characterizations of local and global Nash equilibria. Then an algorithm is shown in order to find all possible Nash equilibrium pairs of locations. The minimization of the social cost leads to a Nash equilibrium. An example shows that there may exist multiple Nash equilibria which are not minimizers of the social cost.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 214 (2011)
Issue (Month): 1 (October)
Contact details of provider:
Web page: http://www.elsevier.com/locate/eor
Location Game theory Nash equilibrium;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Pelegrin, Blas & Michelot, Christian & Plastria, Frank, 1985. "On the uniqueness of optimal solutions in continuous location theory," European Journal of Operational Research, Elsevier, vol. 20(3), pages 327-331, June.
- LABBE, Martine & PEETERS, Dominique & THISSE, Jacques-François, 1993.
"Location on Networks,"
CORE Discussion Papers
1993040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
- Osborne, Martin J & Pitchik, Carolyn, 1987.
"Equilibrium in Hotelling's Model of Spatial Competition,"
Econometric Society, vol. 55(4), pages 911-22, July.
- Martin J Osborne & Carolyn Pitchik, 1985. "Equilibrium in Hotelling's Model of Spatial Competition," Department of Economics Working Papers 1985-02, McMaster University.
- Abellanas, Manuel & López, M Dolores & Rodrigo, Javier, 2010. "Searching for equilibrium positions in a game of political competition with restrictions," European Journal of Operational Research, Elsevier, vol. 201(3), pages 892-896, March.
- Gupta, Barnali, 1994. "Competitive spatial price discrimination with strictly convex production costs," Regional Science and Urban Economics, Elsevier, vol. 24(2), pages 265-272, April.
- d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979.
"On Hotelling's "Stability in Competition","
Econometric Society, vol. 47(5), pages 1145-50, September.
- repec:ner:louvai:info:hdl:2078.1/52714 is not listed on IDEAS
- ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
- Abellanas, Manuel & Lillo, Isabel & Lopez, M Dolores & Rodrigo, Javier, 2006. "Electoral strategies in a dynamical democratic system. Geometric models," European Journal of Operational Research, Elsevier, vol. 175(2), pages 870-878, December.
- repec:fth:erroem:9255-a is not listed on IDEAS
- Hamilton, Jonathan H. & Thisse, Jacques-Francois & Weskamp, Anita, 1989. "Spatial discrimination : Bertrand vs. Cournot in a model of location choice," Regional Science and Urban Economics, Elsevier, vol. 19(1), pages 87-102, February.
- Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-40, May.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.