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Spatial Competition and the Core

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  • Hamilton, Jonathan H.
  • MacLeod, W. Bently
  • Thisse, Jacques-Francois

Abstract

Models of spatial competition have proven to be very useful in describing differentiated products markets. A serious problem is that nonexistence of Nash equilibria seems endemic. This problem is resolved by modelling the price formation process using the core. The equilibrium is the outcome of a two-stage process. In the first stage, two firms Choose locations simultaneously, looking ahead to the second stage. The second stage has prices determined by an allocation in the core of a cooperative subgame allowing for coalitions of buyers and sellers. The price selection is the joint profit maximum for the duopolists. This selection exists for all location pairs and coincides with the pure strategy Nash equilibrium of duopoly competition when the latter exists. Furthermore, these prices approach the competitive level as the distance between the firms goes to zero, thus capturing the essence of duopoly rivalry. For this price selection, in the location game, the two firms establish themselves at the efficient locations--the first and third quartiles.

Suggested Citation

  • Hamilton, Jonathan H. & MacLeod, W. Bently & Thisse, Jacques-Francois, 1987. "Spatial Competition and the Core," Queen's Institute for Economic Research Discussion Papers 275212, Queen's University - Department of Economics.
  • Handle: RePEc:ags:queddp:275212
    DOI: 10.22004/ag.econ.275212
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    1. Drezner, Zvi & Wesolowsky, George O., 1996. "Location-allocation on a line with demand-dependent costs," European Journal of Operational Research, Elsevier, vol. 90(3), pages 444-450, May.
    2. Hamilton, Jonathan & Slutsky, Steven, 2004. "Nonlinear price discrimination with a finite number of consumers and constrained recontracting," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 737-757, June.
    3. Boyer, Marcel & Laffont, Jean-Jacques & Mahenc, Philippe & Moreaux, Michel, 1995. "Sequential Location Equilibria under Incomplete Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 323-350, July.
    4. Stuart, Harborne Jr., 2004. "Efficient spatial competition," Games and Economic Behavior, Elsevier, vol. 49(2), pages 345-362, November.
    5. Ricardo Biscaia & Isabel Mota, 2013. "Models of spatial competition: A critical review," Papers in Regional Science, Wiley Blackwell, vol. 92(4), pages 851-871, November.
    6. Jonathan Vogel, 2011. "Spatial Price Discrimination with Heterogeneous Firms," Journal of Industrial Economics, Wiley Blackwell, vol. 59(4), pages 661-676, December.
    7. Marcus Berliant & Yves Zenou, 2014. "Labor Differentiation and Agglomeration in General Equilibrium," International Regional Science Review, , vol. 37(1), pages 36-65, January.
    8. Byford, Martin C., 2015. "A theoretical foundation for the undercut-proof equilibrium," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 209-220.
    9. Chisholm, Darlene C. & Norman, George, 2004. "Heterogeneous preferences and location choice with multi-product firms," Regional Science and Urban Economics, Elsevier, vol. 34(3), pages 321-339, May.
    10. Reisinger, Markus, 2004. "Two-Sided Markets with Negative Externalities," Discussion Papers in Economics 478, University of Munich, Department of Economics.
    11. Jacques-François Thisse & Suzanne Scotchmer, 1993. "Les implications de l'espace pour la concurrence," Revue Économique, Programme National Persée, vol. 44(4), pages 653-670.
    12. Jan K. Brueckner & Jacques-FranÁois Thisse & Yves Zenou, 2002. "Local Labor Markets, Job Matching, and Urban Location," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(1), pages 155-171, February.
    13. Martin C. Byford, 2018. "Ex-post price stability with convex costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1065-1085, November.
    14. Eleftheriou, Konstantinos & Michelacakis, Nickolas, 2017. "Spatial Price Discrimination and Privatization on Vertically Related Markets," MPRA Paper 76964, University Library of Munich, Germany.
    15. Eleftheriou, Konstantinos & Michelacakis, Nickolas, 2015. "A Unified Model of Spatial Price Discrimination," MPRA Paper 66557, University Library of Munich, Germany.
    16. Konstantinos Eleftheriou & Nickolas J. Michelacakis, 2020. "Location decisions and welfare under spatial price discrimination," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(7), pages 1202-1210, October.
    17. Giulio Bottazzi & Giovanni Dosi & Giorgio Fagiolo, 2001. "On the Ubiquitous Nature of the Agglomeration Economies and their Diverse Determinants: Some Notes," LEM Papers Series 2001/10, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    18. Richard S. Higgins, 1999. "A geometric treatment of discriminatory pricing among spatially competitive suppliers, with antitrust applications," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 20(8), pages 437-445.
    19. F. William McElroy, 1997. "Alternatives to the U.S. Antitrust Agency Approach to Market Definition," Industrial Organization 9706003, University Library of Munich, Germany.
    20. Darlene C. Chisholm & George Norman, 2002. "Spatial Competition and Demand: An Application to Motion Pictures," Discussion Papers Series, Department of Economics, Tufts University 0216, Department of Economics, Tufts University.
    21. A. de Palma & C. Fontan & O. Mekkaoui, 2000. "Trip Timing for Public Transportation : An Empirical Application," THEMA Working Papers 2000-19, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    22. F. William McElroy, 1996. "Alternatives to the U.S. Antitrust Agency Approach to Market Definition," Law and Economics 9606001, University Library of Munich, Germany.

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