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Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies

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  • Tasnádi, Attila

Abstract

We determine the endogenous order of moves in which the firms set their prices in the framework of a capacity-constrained Bertrand-Edgeworth triopoly. A three-period timing game that determines the period in which the firms announce their prices precedes the price-setting stage. We show for the non-trivial case (in which the Bertrand-Edgeworth triopoly has only an equilibrium in non-degenerated mixedstrategies) that the firm with the largest capacity sets its price first, while the two other firms set their prices later. Our result extends a finding by Deneckere and Kovenock (1992) from duopolies to triopolies. This extension was made possible by Hirata's (2009) recent advancements on the mixed-strategy equilibria of Bertrand-Edgeworth games.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47610.

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Date of creation: 27 Dec 2012
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Handle: RePEc:pra:mprapa:47610

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Keywords: Bertrand-Edgeworth; price leadership; oligopoly; timing games;

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References

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  1. van Damme, Eric & Hurkens, Sjaak, 2004. "Endogenous price leadership," Games and Economic Behavior, Elsevier, Elsevier, vol. 47(2), pages 404-420, May.
  2. Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.
  3. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-22, February.
  4. Allen, Beth & Hellwig, Martin, 1993. "Bertrand-Edgeworth Duopoly with Proportional Residual Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 39-60, February.
  5. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, Elsevier, vol. 38(2), pages 238-260, April.
  6. De Francesco, Massimo A. & Salvadori, Neri, 2008. "Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly," MPRA Paper 10767, University Library of Munich, Germany, revised 26 Sep 2008.
  7. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 2(1), pages 29-46, March.
  8. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
  9. Bagh, Adib, 2010. "Variational convergence: Approximation and existence of equilibria in discontinuous games," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(3), pages 1244-1268, May.
  10. Deneckere, Raymond J & Kovenock, Dan, 1992. "Price Leadership," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 59(1), pages 143-62, January.
  11. Gal-Or, Esther, 1985. "First Mover and Second Mover Advantages," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 649-53, October.
  12. Eric van Damme & Sjaak Hurkens, 1996. "Endogenous Stackelberg leadership," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 190, Department of Economics and Business, Universitat Pompeu Fabra.
  13. de Frutos, Maria-Angeles & Fabra, Natalia, 2007. "Endogenous Capacities and Price Competition: The Role of Demand Uncertainty," CEPR Discussion Papers, C.E.P.R. Discussion Papers 6096, C.E.P.R. Discussion Papers.
  14. Makoto Yano & Takashi Komatsubara, 2006. "Endogenous price leadership and technological differences," International Journal of Economic Theory, The International Society for Economic Theory, The International Society for Economic Theory, vol. 2(3-4), pages 365-383.
  15. Matsumura, Toshihiro, 1999. "Quantity-setting oligopoly with endogenous sequencing," International Journal of Industrial Organization, Elsevier, Elsevier, vol. 17(2), pages 289-296, February.
  16. Steve Dowrick, 1986. "von Stackelberg and Cournot Duopoly: Choosing Roles," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 251-260, Summer.
  17. Reynolds, Stanley S. & Wilson, Bart J., 2000. "Bertrand-Edgeworth Competition, Demand Uncertainty, and Asymmetric Outcomes," Journal of Economic Theory, Elsevier, Elsevier, vol. 92(1), pages 122-141, May.
  18. Hviid, Morten, 1991. "Capacity constrained duopolies, uncertain demand and non-existence of pure strategy equilibria," European Journal of Political Economy, Elsevier, Elsevier, vol. 7(2), pages 183-190, July.
  19. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, Elsevier, vol. 21(2), pages 113-116.
  20. von Stengel, Bernhard, 2010. "Follower payoffs in symmetric duopoly games," Games and Economic Behavior, Elsevier, Elsevier, vol. 69(2), pages 512-516, July.
  21. Hirata Daisuke, 2009. "Asymmetric Bertrand-Edgeworth Oligopoly and Mergers," The B.E. Journal of Theoretical Economics, De Gruyter, De Gruyter, vol. 9(1), pages 1-25, July.
  22. Makoto Yano & Takashi Komatsubara, 2012. "Price Competition or Tacit Collusion," KIER Working Papers, Kyoto University, Institute of Economic Research 807, Kyoto University, Institute of Economic Research.
  23. Krishnendu G. Dastidar & Dave Furth, 2005. "Endogenous price leadership in a duopoly: Equal products, unequal technology," International Journal of Economic Theory, The International Society for Economic Theory, The International Society for Economic Theory, vol. 1(3), pages 189-210.
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