IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/47610.html
   My bibliography  Save this paper

Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies

Author

Listed:
  • 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.

Suggested Citation

  • Tasnádi, Attila, 2012. "Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies," MPRA Paper 47610, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:47610
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/47610/1/MPRA_paper_47610.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
    2. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    3. Reynolds, Stanley S. & Wilson, Bart J., 2000. "Bertrand-Edgeworth Competition, Demand Uncertainty, and Asymmetric Outcomes," Journal of Economic Theory, Elsevier, vol. 92(1), pages 122-141, May.
    4. 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, vol. 26(3), pages 649-653, October.
    5. van Damme, Eric & Hurkens, Sjaak, 2004. "Endogenous price leadership," Games and Economic Behavior, Elsevier, vol. 47(2), pages 404-420, May.
    6. van Damme, Eric & Hurkens, Sjaak, 1999. "Endogenous Stackelberg Leadership," Games and Economic Behavior, Elsevier, vol. 28(1), pages 105-129, July.
    7. 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, vol. 13(1), pages 111-122, February.
    8. 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, vol. 1(3), pages 189-210, September.
    9. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    10. Alexei F. Cheviakov & John M. Hartwick, 2005. "Beckmann'S Edgeworth-Bertrand Duopoly Example Revisited," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 461-472.
    11. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    12. Raymond J. Deneckere & Dan Kovenock, 1992. "Price Leadership," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 143-162.
      • Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.
    14. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 27-41.
    15. de Frutos, María-Ángeles & Fabra, Natalia, 2011. "Endogenous capacities and price competition: The role of demand uncertainty," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 399-411, July.
    16. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    17. Hviid, Morten, 1991. "Capacity constrained duopolies, uncertain demand and non-existence of pure strategy equilibria," European Journal of Political Economy, Elsevier, vol. 7(2), pages 183-190, July.
    18. 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.
    19. Deneckere, Raymond J & Kovenock, Dan & Lee, Robert, 1992. "A Model of Price Leadership Based on Consumer Loyalty," Journal of Industrial Economics, Wiley Blackwell, vol. 40(2), pages 147-156, June.
    20. van Damme, Eric & Hurkens, Sjaak, 1999. "Endogenous Stackelberg Leadership," Games and Economic Behavior, Elsevier, vol. 28(1), pages 105-129, July.
    21. Toshihiro Matsumura, 2002. "Market Instability in a Stackelberg Duopoly," Journal of Economics, Springer, vol. 75(3), pages 199-210, April.
    22. Makoto Yano & Takashi Komatsubara, 2006. "Endogenous price leadership and technological differences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(3‐4), pages 365-383, September.
    23. von Stengel, Bernhard, 2010. "Follower payoffs in symmetric duopoly games," Games and Economic Behavior, Elsevier, vol. 69(2), pages 512-516, July.
    24. Matsumura, Toshihiro, 1999. "Quantity-setting oligopoly with endogenous sequencing," International Journal of Industrial Organization, Elsevier, vol. 17(2), pages 289-296, February.
    25. Steve Dowrick, 1986. "von Stackelberg and Cournot Duopoly: Choosing Roles," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 251-260, Summer.
    26. 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, vol. 34(1), pages 39-60, February.
    27. Bagh, Adib, 2010. "Variational convergence: Approximation and existence of equilibria in discontinuous games," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1244-1268, May.
    28. Hirata Daisuke, 2009. "Asymmetric Bertrand-Edgeworth Oligopoly and Mergers," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-25, July.
    29. Makoto Yano & Takashi Komatsubara, 2012. "Price Competition or Tacit Collusion," KIER Working Papers 807, Kyoto University, Institute of Economic Research.
    30. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    2. De Francesco, Massimo A. & Salvadori, Neri, 2016. "Bertrand-Edgeworth games under triopoly: the equilibrium strategies when the payoffs of the two smallest firms are proportional to their capacities," MPRA Paper 69999, University Library of Munich, Germany.
    3. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.
    4. Jacobs, Martin & Requate, Till, 2016. "Bertrand-Edgeworth markets with increasing marginal costs and voluntary trading: Experimental evidence," Economics Working Papers 2016-01, Christian-Albrechts-University of Kiel, Department of Economics.
    5. Kujal, Praveen & García Díaz, Antón, 1998. "List princing and pure strategy outcomes in a bertrand edgeworth duopoly," UC3M Working papers. Economics 6089, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Tamás Balogh & Attila Tasnádi, 2012. "Does timing of decisions in a mixed duopoly matter?," Journal of Economics, Springer, vol. 106(3), pages 233-249, July.
    7. Jacobs, Martin & Requate, Till, 2016. "Demand rationing in Bertrand-Edgeworth markets with fixed capacities: An experiment," Economics Working Papers 2016-03, Christian-Albrechts-University of Kiel, Department of Economics.
    8. Roy Chowdhury, Prabal, 2008. "Bertrand-Edgeworth equilibrium with a large number of firms," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 746-761, May.
    9. Matsui, Kenji, 2016. "Asymmetric product distribution between symmetric manufacturers using dual-channel supply chains," European Journal of Operational Research, Elsevier, vol. 248(2), pages 646-657.
    10. Victor Martínez-de-Albéniz & Kalyan Talluri, 2011. "Dynamic Price Competition with Fixed Capacities," Management Science, INFORMS, vol. 57(6), pages 1078-1093, June.
    11. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    12. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium: Manipulable residual demand," Discussion Papers 04-15, Indian Statistical Institute, Delhi.
    13. Salvadori, Neri & De Francesco, Massimo A., 2020. "Bertrand-Edgeworth oligopoly: Characterization of mixed strategy equilibria when some firms are large and the others are small," MPRA Paper 102274, University Library of Munich, Germany.
    14. Amir, Rabah & Stepanova, Anna, 2006. "Second-mover advantage and price leadership in Bertrand duopoly," Games and Economic Behavior, Elsevier, vol. 55(1), pages 1-20, April.
    15. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium with a large number of firms," Discussion Papers 04-12, Indian Statistical Institute, Delhi.
    16. Daisuke Hirata & Toshihiro Matsumura, 2011. "Price leadership in a homogeneous product market," Journal of Economics, Springer, vol. 104(3), pages 199-217, November.
    17. Tasnádi, Attila, 2001. "A Bertrand-Edgeworth-oligopóliumok. Irodalmi áttekintés [Bertrand-Edgeworth oligopolies - a survey of the literature]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1081-1092.
    18. Simon Loertscher, 2008. "Market Making Oligopoly," Journal of Industrial Economics, Wiley Blackwell, vol. 56(2), pages 263-289, June.
    19. Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.
    20. Zhiqi Chen & Gang Li, 2018. "Horizontal Mergers In The Presence Of Capacity Constraints," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1346-1356, April.

    More about this item

    Keywords

    Bertrand-Edgeworth; price leadership; oligopoly; timing games;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:47610. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.