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Nash versus consistent equilibrium: A comparative perspective on a mixed duopoly location model of spatial price discrimination with delegation

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  • Michelacakis, Nickolas J.

Abstract

We argue that under the presence of a public firm, discriminatory pricing according to location leads to an efficient consistent equilibrium. We consider a mixed ownership duopoly delegation model with spatial price discrimination and constant, albeit different, marginal production costs. In contrast to what holds true for a private duopoly, we prove that the Nash equilibrium, absent delegation, is both consistent and socially optimal. The consistent equilibrium remains socially optimal regardless of the order in the delegation process. Under Nash conjectures, in most cases, firm owners have a strong incentive to delegate location decisions to managers. In such cases, duopolists locate closer to each other. Nash, compared to consistency of conjectures, leads to lower prices, lower profits, for both firms, and increased surplus for the consumer. The result surprises as it contrasts with respective findings regarding a private duopoly.

Suggested Citation

  • Michelacakis, Nickolas J., 2023. "Nash versus consistent equilibrium: A comparative perspective on a mixed duopoly location model of spatial price discrimination with delegation," Regional Science and Urban Economics, Elsevier, vol. 99(C).
    • Handle: RePEc:eee:regeco:v:99:y:2023:i:c:s0166046222000989
    DOI: 10.1016/j.regsciurbeco.2022.103860
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    1. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-640, May.
    2. Perloff,Jeffrey M. & Karp,Larry S. & Golan,Amos, 2007. "Estimating Market Power and Strategies," Cambridge Books, Cambridge University Press, number 9780521011143.
    3. Boyer, Marcel & Moreaux, Michel, 1983. "Consistent versus Non-Consistent Conjectures in Doupoly Theory: Some Examples," Journal of Industrial Economics, Wiley Blackwell, vol. 32(1), pages 97-110, September.
    4. Cremer, Helmuth & Marchand, Maurice & Thisse, Jacques-Francois, 1991. "Mixed oligopoly with differentiated products," International Journal of Industrial Organization, Elsevier, vol. 9(1), pages 43-53, March.
    5. Itaya, Jun-ichi & Shimomura, Koji, 2001. "A dynamic conjectural variations model in the private provision of public goods: a differential game approach," Journal of Public Economics, Elsevier, vol. 81(1), pages 153-172, July.
    6. repec:bla:econom:v:48:y:1981:i:189:p:79-86 is not listed on IDEAS
    7. Barros, Fatima, 1995. "Incentive schemes as strategic variables: An application to a mixed duopoly," International Journal of Industrial Organization, Elsevier, vol. 13(3), pages 373-386, September.
    8. Vickers, John, 1985. "Delegation and the Theory of the Firm," Economic Journal, Royal Economic Society, vol. 95(380a), pages 138-147, Supplemen.
    9. Fershtman, Chaim & Judd, Kenneth L, 1987. "Equilibrium Incentives in Oligopoly," American Economic Review, American Economic Association, vol. 77(5), pages 927-940, December.
    10. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    11. Toshihiro Matsumura & Noriaki Matsushima, 2003. "Mixed Duopoly with Product Differentiation: Sequential Choice of Location," Australian Economic Papers, Wiley Blackwell, vol. 42(1), pages 18-34, March.
    12. Marc Escrihuela-Villar & Carlos Gutiérrez-Hita, 2019. "On competition and welfare enhancing policies in a mixed oligopoly," Journal of Economics, Springer, vol. 126(3), pages 259-274, April.
    13. Steven D. Sklivas, 1987. "The Strategic Choice of Managerial Incentives," RAND Journal of Economics, The RAND Corporation, vol. 18(3), pages 452-458, Autumn.
    14. Sugden, Robert, 1985. "Consistent conjectures and voluntary contributions to public goods: why the conventional theory does not work," Journal of Public Economics, Elsevier, vol. 27(1), pages 117-124, June.
    15. Cyert, Richard M & DeGroot, Morris H, 1973. "An Analysis of Cooperation and Learning in a Duopoly Context," American Economic Review, American Economic Association, vol. 63(1), pages 24-37, March.
    16. John S. Heywood & Guangliang Ye, 2009. "Mixed Oligopoly, Sequential Entry, And Spatial Price Discrimination," Economic Inquiry, Western Economic Association International, vol. 47(3), pages 589-597, July.
    17. Cabral, Luis M. B., 1995. "Conjectural variations as a reduced form," Economics Letters, Elsevier, vol. 49(4), pages 397-402, October.
    18. Braid, Ralph M., 2008. "Spatial price discrimination and the locations of firms with different product selections or product varieties," Economics Letters, Elsevier, vol. 98(3), pages 342-347, March.
    19. Heywood, John S. & Ye, Guangliang, 2009. "Mixed oligopoly and spatial price discrimination with foreign firms," Regional Science and Urban Economics, Elsevier, vol. 39(5), pages 592-601, September.
    20. A. P. Lerner & H. W. Singer, 1937. "Some Notes on Duopoly and Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 45(2), pages 145-145.
    21. Li, Mingzhi & Lien, Jaimie W. & Zheng, Jie, 2021. "Optimal subsidies in the competition between private and state-owned enterprises," International Review of Economics & Finance, Elsevier, vol. 76(C), pages 1235-1244.
    22. Bresnahan, Timothy F, 1981. "Duopoly Models with Consistent Conjectures," American Economic Review, American Economic Association, vol. 71(5), pages 934-945, December.
    23. Scrimitore, Marcella, 2013. "Price or quantity? The strategic choice of subsidized firms in a mixed duopoly," Economics Letters, Elsevier, vol. 118(2), pages 337-341.
    24. John Heywood & Zheng Wang, 2016. "Consistent location conjectures under spatial price discrimination," Journal of Economics, Springer, vol. 117(2), pages 167-180, March.
    25. Matsumura, Toshihiro & Ogawa, Akira, 2012. "Price versus quantity in a mixed duopoly," Economics Letters, Elsevier, vol. 116(2), pages 174-177.
    26. Matsushima, Noriaki & Matsumura, Toshihiro, 2006. "Mixed oligopoly, foreign firms, and location choice," Regional Science and Urban Economics, Elsevier, vol. 36(6), pages 753-772, November.
    27. Edgar M. Hoover, 1937. "Spatial Price Discrimination," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(3), pages 182-191.
    28. de Fraja, Giovanni & Delbono, Flavio, 1989. "Alternative Strategies of a Public Enterprise in Oligopoly," Oxford Economic Papers, Oxford University Press, vol. 41(2), pages 302-311, April.
    29. Escrihuela-Villar Marc, 2015. "A Note on the Equivalence of the Conjectural Variations Solution and the Coefficient of Cooperation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(2), pages 473-480, July.
    30. Beladi, Hamid & Chakrabarti, Avik & Marjit, Sugata, 2014. "A public firm in a model of spatial duopoly with price discrimination," Economics Letters, Elsevier, vol. 123(1), pages 79-81.
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    Cited by:

    1. Park, Junseok & Moon, Ilkyeong, 2023. "A facility location problem in a mixed duopoly on networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).

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    More about this item

    Keywords

    Mixed duopoly; Delegation; Spatial competition; Consistent conjectures; Nash equilibrium;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L21 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Business Objectives of the Firm
    • L22 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Organization and Market Structure
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • R32 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - Other Spatial Production and Pricing Analysis

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