The Annals of Regional Science

, Volume 44, Issue 2, pp 377–407 | Cite as

Spatial Cournot equilibrium: do branches matter?

  • Santiago Carbó Valverde
  • Miguel Ángel Fortes Escalona
Original Paper


This paper aims to contribute to the literature of Cournot spatial equilibria in two-dimensional spaces by considering branching. We study the case in which two firms compete on a circle and each one has the possibility of opening one or more branches. An innovative method—polar coordinates—is employed to obtain the complex profit functions. We show that there exists a symmetric subgame perfect Nash equilibrium where both firms place their n branches alternately and at the same distance from the center of the circle. Additionally, we show that this is, up to rotation, the unique symmetric equilibrium location.

JEL Classification

D43 L13 


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  1. Anderson SP, Neven DJ (1991) Cournot competition yields spatial agglomeration. Int Econ Rev 32: 793–808CrossRefGoogle Scholar
  2. Berenguer MI, Carbó S, Fortes MA (2005) Cournot competition in a two-dimensional circular city. Manchester Sch 73: 40–49CrossRefGoogle Scholar
  3. Bradley G, Smith KJ (1995) Calculus, vol 2. Prentice-Hall, Inc., Englewood CliffsGoogle Scholar
  4. Caplin A, Nalebuff B (1991) Aggregation and imperfect competition: on the existence of equilibrium. Econometrica 59: 25–59CrossRefGoogle Scholar
  5. Chamorro Rivas JM (2000a) Plant proliferation in a spatial model of Cournot competiton. Reg Sci Urban Econ 30: 507–518CrossRefGoogle Scholar
  6. Chamorro Rivas JM (2000b) Spatial dispersion in Cournot competition. Spanish Econ Rev 2: 145–152CrossRefGoogle Scholar
  7. D’Aspremont C, Jaskold-Gabszewick J, Thisse JF (1979) On Hotelling’s stability in competition. Econometrica 47: 1145–1150CrossRefGoogle Scholar
  8. De Frutos MA, Hamoudi H, Jarque X (2002) Spatial competition with concave transport costs. Reg Sci Urban Econ 32: 531–540CrossRefGoogle Scholar
  9. Dorta-González P, Santos-Peñate DR, Suárez-Vega R (2004) Cournot oligopolistic competition in spatially separated markets: the Stackelberg equilibrium. Ann Reg Sci 38: 499–511CrossRefGoogle Scholar
  10. Economides N (1986) Nash equilibrium in duopoly with products defined by two characteristics. Rand J Econ 17: 431–439CrossRefGoogle Scholar
  11. Gupta B, Lai F, Pal D, Sarkar J, Yu C (2004) Where to locate in a circular city?. Int J Ind Organ 22: 759–782CrossRefGoogle Scholar
  12. Hamilton JH, Thisse JF, Weskamp A (1989) Spatial discrimination: Bertrand vs. Cournot in a model of location choice. Reg Sci Urban Econ 19: 87–102CrossRefGoogle Scholar
  13. Hotelling H (1929) Stability in competition. Econ J 39: 41–57CrossRefGoogle Scholar
  14. Labbé M, Hakimi SL (1991) Market and location equilibrium for two competitors. Oper Res 39(5): 749–756CrossRefGoogle Scholar
  15. Lederer PJ, Hurter AP Jr (1986) Competition of firms: discriminatory pricing and location. Econometrica 54: 623–640CrossRefGoogle Scholar
  16. Lerner AP, Singer HW (1939) Some notes on duopoly and spatial competition. J Polit Econ 45: 145–186CrossRefGoogle Scholar
  17. Lucas RE Jr, Rossi-Hansberg E (2002) On the internal structure of cities. Econometrica 70(4): 1445–1476CrossRefGoogle Scholar
  18. Martínez-Giralt X, Neven DJ (1988) Can price competition dominate market segmentation?. J Ind Econ 36(4): 431–442CrossRefGoogle Scholar
  19. Matsushima N (2001) Cournot competition and spatial agglomeration revisited. Econ Lett 73: 175–177CrossRefGoogle Scholar
  20. Pal D (1998) Does Cournot competition yield spatial agglomeration?. Econ Lett 60: 49–53CrossRefGoogle Scholar
  21. Pal D, Sarkar J (2002) Spatial competition among multi-store firms. Int J Ind Organ 20: 163–190CrossRefGoogle Scholar
  22. Salop SC (1979) Monopolistic competition with outside goods. Bell J Econ 10: 141–156CrossRefGoogle Scholar
  23. Sarkar J, Gupta B, Pal D (1997) Location equilibrium for Cournot oligopoly in spatially separated markets. J Reg Sci 37(2): 195–212CrossRefGoogle Scholar
  24. Tabuchi T (1994) Two-stage two-dimensional spatial competition between two firms. Reg Sci Urban Econ 24: 207–227CrossRefGoogle Scholar
  25. Teitz MB (1968) Locational strategies for competitive systems. J Reg Sci 8(2): 135–148CrossRefGoogle Scholar
  26. Thill J-C (1992) Competitive strategies for multi-establishment firms. Econ Geograph 68: 361–382Google Scholar
  27. Thill J-C (1997) Multi-outlet firms, competition and market segmentation strategies. Reg Sci Urban Econ 27: 67–86CrossRefGoogle Scholar
  28. Thill J-C (2000) Network competition and branch differentiation with consumer heterogeneity. Ann Reg Sci 34: 451–468CrossRefGoogle Scholar
  29. Vickrey WS (1964) Microstatics, Harcourt, Brace and World, New York. Republished as Spatial competition, monopolistic competition, and optimal product diversity. Int J Ind Organ 17:953–963 (1999)Google Scholar
  30. Yu C, Lai F (2003) Cournot competiton in spatial markets: some further results. Pap Reg Sci 82: 569–580CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Santiago Carbó Valverde
    • 1
  • Miguel Ángel Fortes Escalona
    • 2
  1. 1.Departamento de Teoría e Historia Económica, Facultad de Ciencias Económicas y EmpresarialesUniversidad de GranadaGranadaSpain
  2. 2.Departamento de Matemática Aplicada, Facultad de Ciencias Económicas y EmpresarialesUniversidad de GranadaGranadaSpain

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