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Price Competition on Graphs

Author

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  • Pim Heijnen

    (University of Groningen)

  • Adriaan Soetevent

    (University of Groningen)

Abstract

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more generally for all graph models with two or more firms that cannot be reduced to a line or circle.

Suggested Citation

  • Pim Heijnen & Adriaan Soetevent, 2014. "Price Competition on Graphs," Tinbergen Institute Discussion Papers 14-131/VII, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20140131
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    1. Bollobas, Bela & Stern, Nicholas, 1972. "The optimal structure of market areas," Journal of Economic Theory, Elsevier, vol. 4(2), pages 174-179, April.
    2. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    3. Michael Noel, 2009. "Do retail gasoline prices respond asymmetrically to cost shocks? The influence of Edgeworth Cycles," RAND Journal of Economics, RAND Corporation, vol. 40(3), pages 582-595, September.
    4. Matthew S. Lewis, 2011. "Asymmetric Price Adjustment and Consumer Search: An Examination of the Retail Gasoline Market," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 20(2), pages 409-449, June.
    5. Michael D. Noel, 2007. "Edgeworth Price Cycles: Evidence From The Toronto Retail Gasoline Market," Journal of Industrial Economics, Wiley Blackwell, vol. 55(1), pages 69-92, March.
    6. Bloch, Francis & Quérou, Nicolas, 2013. "Pricing in social networks," Games and Economic Behavior, Elsevier, vol. 80(C), pages 243-261.
    7. Irmen, Andreas & Thisse, Jacques-Francois, 1998. "Competition in Multi-characteristics Spaces: Hotelling Was Almost Right," Journal of Economic Theory, Elsevier, vol. 78(1), pages 76-102, January.
    8. von Ungern-Sternberg, Thomas, 1991. "Monopolistic Competition on the Pyramid," Journal of Industrial Economics, Wiley Blackwell, vol. 39(4), pages 355-368, June.
    9. Michael D. Noel, 2007. "Edgeworth Price Cycles, Cost-Based Pricing, and Sticky Pricing in Retail Gasoline Markets," The Review of Economics and Statistics, MIT Press, vol. 89(2), pages 324-334, May.
    10. Nicholas Economides, 1986. "Nash Equilibrium in Duopoly with Products Defined by Two Characteristics," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 431-439, Autumn.
    11. Jean-Francois Houde, 2012. "Spatial Differentiation and Vertical Mergers in Retail Markets for Gasoline," American Economic Review, American Economic Association, vol. 102(5), pages 2147-2182, August.
    12. Eaton, B Curtis & Lipsey, Richard G, 1976. "The Non-Uniqueness of Equilibrium in the Loschian Location Model," American Economic Review, American Economic Association, vol. 66(1), pages 71-93, March.
    13. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    14. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Post-Print halshs-00983085, HAL.
    15. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    16. Picone, Gabriel A. & Ridley, David B. & Zandbergen, Paul A., 2009. "Distance decreases with differentiation: Strategic agglomeration by retailers," International Journal of Industrial Organization, Elsevier, vol. 27(3), pages 463-473, May.
    17. Matthew Lewis & Michael Noel, 2011. "The Speed of Gasoline Price Response in Markets with and without Edgeworth Cycles," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 672-682, May.
    18. Raith, Michael, 1996. "Spatial retail markets with commuting consumers," International Journal of Industrial Organization, Elsevier, vol. 14(4), pages 447-463, June.
    19. JASKOLD GABSZEWICZ, Jean & THISSE, Jacques-François, 1986. "Spatial competition and the location of firms," LIDAM Reprints CORE 713, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    21. Holahan, William L & Schuler, Richard E, 1981. "The Welfare Effects of Market Shapes in the Loschian Location Model: Squares vs. Hexagons [The Non-Uniqueness of Equilibrium in the Loschian Location Model]," American Economic Review, American Economic Association, vol. 71(4), pages 738-746, September.
    22. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    23. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    24. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    25. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    26. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
    27. Edwin S. Mills & Michael R. Lav, 1964. "A Model of Market Areas with Free Entry," Journal of Political Economy, University of Chicago Press, vol. 72(3), pages 278-278.
    28. Lance J. Bachmeier & James M. Griffin, 2003. "New Evidence on Asymmetric Gasoline Price Responses," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 772-776, August.
    29. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
    30. Castanias, Rick & Johnson, Herb, 1993. "Gas Wars: Retail Gasoline Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 171-174, February.
    31. Nicolas de Roos & Hajime Katayama, 2013. "Gasoline Price Cycles Under Discrete Time Pricing," The Economic Record, The Economic Society of Australia, vol. 89(285), pages 175-193, June.
    32. Francis Bloch & Nicolas Quérou, 2008. "Pricing in networks," Working Papers hal-00356356, HAL.
    33. Zhongmin Wang, 2009. "(Mixed) Strategy in Oligopoly Pricing: Evidence from Gasoline Price Cycles Before and Under a Timing Regulation," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 987-1030, December.
    34. repec:hal:pseose:hal-01013603 is not listed on IDEAS
    35. Eckert, Andrew, 2003. "Retail price cycles and the presence of small firms," International Journal of Industrial Organization, Elsevier, vol. 21(2), pages 151-170, February.
    36. Greenhut, M L & Hwang, M J & Ohta, H, 1976. "An Empirical Evaluation of the Equilibrium Size and Shape of Market Areas," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 172-190, February.
    37. Michael D. Noel, 2011. "Edgeworth price cycles," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
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    Cited by:

    1. Hinloopen, Jeroen & Müller, Wieland & Normann, Hans-Theo, 2014. "Output commitment through product bundling: Experimental evidence," European Economic Review, Elsevier, vol. 65(C), pages 164-180.
    2. Hinloopen, Jeroen & Martin, Stephen, 2017. "Costly location in Hotelling duopoly," Research in Economics, Elsevier, vol. 71(1), pages 118-128.
    3. Fernando Vega-Redondo & Paolo Pin & Diego Ubfal & Cristiana Benedetti-Fasil & Charles Brummitt & Gaia Rubera & Dirk Hovy & Tommaso Fornaciari, 2019. "Peer Networks and Entrepreneurship: a Pan-African RCT," Working Papers 648, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Gaëtan Fournier & Marco Scarsini, 2019. "Location Games on Networks: Existence and Efficiency of Equilibria," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 212-235, February.
    5. de Roos, Nicolas, 2012. "Static models of the Edgeworth cycle," Economics Letters, Elsevier, vol. 117(3), pages 881-882.
    6. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Post-Print halshs-00983085, HAL.
    7. Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks a practitioner guide," Working Papers hal-02173210, HAL.
    8. Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks, a practitioner's guide," Papers 1907.02320, arXiv.org, revised Aug 2019.
    9. Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks a practitioner guide," SciencePo Working papers Main hal-02173210, HAL.
    10. Dubovik, Andrei, 2018. "Mergers on Networks," MPRA Paper 95458, University Library of Munich, Germany.

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    More about this item

    Keywords

    spatial competition; Hotelling; graphs;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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