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Endougenous Timing in a Mixed Duopoly

  • Rabah Amir

    ()

    (Department of Economics, University of Arizona)

  • Giuseppe De Feo

    ()

    (Department of Economics, University of Pavia)

This paper applies the framework of endogenous timing in games to mixed quantity duopoly, wherein a private – domestic or foreign – firm competes with a public, welfare maximizing firm. We show that simultaneous play never emerges as a subgame-perfect equilibrium of the extended game, in sharp contrast to private duopoly games. We provide sufficient conditions for the emergence of public and/or private leadership equilibrium. In all cases, private profits and social welfare are higher than under the corresponding Cournot equilibrium. From a methodological viewpoint we make extensive use of the basic results from the theory of supermodular games in order to avoid common extraneous assumptions such as concavity, existence and uniqueness of the different equilibria, whenever possible. Some policy implications are drawn, in particular those relating to the merits of privatization.

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File URL: http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/wpaper/q162.pdf
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Paper provided by University of Pavia, Department of Economics and Quantitative Methods in its series Quaderni di Dipartimento with number 162.

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Length: 34 pages
Date of creation: Feb 2012
Date of revision:
Handle: RePEc:pav:wpaper:162
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  1. CREMER, Helmuth & MARCHAND, Maurice & THISSE, Jacques-François, . "The public firm as an instrument for regulating an oligopolistic market," CORE Discussion Papers RP -832, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Hellwig, Martin & Leininger, Wolfgang, 1987. "On the existence of subgame-perfect equilibrium in infinite-action games of perfect information," Journal of Economic Theory, Elsevier, vol. 43(1), pages 55-75, October.
  3. Bernhard von Stengel & Shmuel Zamir, 2010. "Leadership games with convex strategy sets," LSE Research Online Documents on Economics 27653, London School of Economics and Political Science, LSE Library.
  4. de Fraja, Giovanni & Delbono, Flavio, 1990. " Game Theoretic Models of Mixed Oligopoly," Journal of Economic Surveys, Wiley Blackwell, vol. 4(1), pages 1-17.
  5. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  6. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  7. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  8. Amir, R., 1991. "Sensitivity analysis of multi-sector optimal economic dynamics," CORE Discussion Papers 1991006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  10. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 85-98, January.
  11. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  12. Lorenz NETT, 1993. "Mixed Oligopoly With Homogeneous Goods," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 64(3), pages 367-393, 07.
  13. Pal, Debashis, 1998. "Endogenous timing in a mixed oligopoly," Economics Letters, Elsevier, vol. 61(2), pages 181-185, November.
  14. de Fraja, Giovanni & Delbono, Flavio, 1989. "Alternative Strategies of a Public Enterprise in Oligopoly," Oxford Economic Papers, Oxford University Press, vol. 41(2), pages 302-11, April.
  15. von Stengel, Bernhard, 2010. "Follower payoffs in symmetric duopoly games," Games and Economic Behavior, Elsevier, vol. 69(2), pages 512-516, July.
  16. Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
  17. Kenneth Fjell & Debashis Pal, 1996. "A Mixed Oligopoly in the Presence of Foreign Private Firms," Canadian Journal of Economics, Canadian Economics Association, vol. 29(3), pages 737-43, August.
  18. Toshihiro Matsumura, 2003. "Stackelberg Mixed Duopoly with a Foreign Competitor," Bulletin of Economic Research, Wiley Blackwell, vol. 55(3), pages 275-287, 07.
  19. Bernhard von Stengel, 2010. "Follower payoffs in symmetric duopoly games," LSE Research Online Documents on Economics 27651, London School of Economics and Political Science, LSE Library.
  20. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
  21. Debashis Pal & Mark D. White, 1998. "Mixed Oligopoly, Privatization, and Strategic Trade Policy," Southern Economic Journal, Southern Economic Association, vol. 65(2), pages 264-281, October.
  22. Fjell, Kenneth & Heywood, John S, 2002. "Public Stackelberg Leadership in a Mixed Oligopoly with Foreign Firms," Australian Economic Papers, Wiley Blackwell, vol. 41(3), pages 267-81, September.
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