IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/4249.html

Go For Broke or Play it Safe? Dynamic Competition with Choice of Variance

Author

Listed:
  • Cabral, Luis
  • Anderson, Axel

Abstract

We consider a differential game in which the joint choices of the two players influences the variance, but not the mean, of the one-dimensional state variable. We interpret this state variable as a summary of how far ?ahead? player 1 is in the game. At each moment in time, players receive a flow pay-off which is a continuous, monotonic and bounded function of the state variable. We show that a Markov Perfect Equilibrium exists and has the property that patient players chose to play it safe when sufficiently ahead and to take risks when sufficiently behind. We also provide a simple condition that implies both players choose risky strategies when neither one is too far ahead, a situation that ensures a dominant player emerges ?quickly?.

Suggested Citation

  • Cabral, Luis & Anderson, Axel, 2004. "Go For Broke or Play it Safe? Dynamic Competition with Choice of Variance," CEPR Discussion Papers 4249, Centre for Economic Policy Research.
    • Handle: RePEc:cpr:ceprdp:4249
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP4249
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tarun Khanna & Marco Iansiti, 1997. "Firm Asymmetries and Sequential R&D: Theory and Evidence from the Mainframe Computer Industry," Management Science, INFORMS, vol. 43(4), pages 405-421, April.
    2. Luís M. B. Cabral, 2003. "R&D Competition when firms Choose Variance," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 12(1), pages 139-150, March.
    3. Johannes Hörner, 2004. "A Perpetual Race to Stay Ahead," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 1065-1088.
    4. Christopher Budd & Christopher Harris & John Vickers, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 543-573.
    5. Cabral, Luis M. B., 2002. "Increasing Dominance with No Efficiency Effect," Journal of Economic Theory, Elsevier, vol. 102(2), pages 471-479, February.
    6. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, December.
    7. Kenneth L. Judd, 2003. "Closed-loop equilibrium in a multi-stage innovation race," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 673-695, March.
    8. Harris, C., 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 44, Boston University - Industry Studies Programme.
    9. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    10. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 1-26, Spring.
    11. Bergemann, Dirk & Valimaki, Juuso, 2002. "Entry and Vertical Differentiation," Journal of Economic Theory, Elsevier, vol. 106(1), pages 91-125, September.
    12. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 1-21.
    13. Bergin, James & MacLeod, W Bentley, 1993. "Continuous Time Repeated Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
    14. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    15. Sudipto Bhattacharya & Dilip Mookherjee, 1986. "Portfolio Choice in Research and Development," RAND Journal of Economics, The RAND Corporation, vol. 17(4), pages 594-605, Winter.
    16. Chaim Fershtman & Ariel Pakes, 2000. "A Dynamic Oligopoly with Collusion and Price Wars," RAND Journal of Economics, The RAND Corporation, vol. 31(2), pages 207-236, Summer.
    17. Dutta, P.K., 1991. "What Do Discounted Optima Converge To? A Theory of Discount Rate Asymptotics in Economic Models," RCER Working Papers 264, University of Rochester - Center for Economic Research (RCER).
    18. Cabral, Luis M B & Riordan, Michael H, 1994. "The Learning Curve, Market Dominance, and Predatory Pricing," Econometrica, Econometric Society, vol. 62(5), pages 1115-1140, September.
    19. Tor Klette & David de Meza, 1986. "Is the Market Biased Against Risky R&D?," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 133-139, Spring.
    20. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    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. Liad Wagman & Vincent Conitzer, 2012. "Choosing fair lotteries to defeat the competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 91-129, February.
    2. Nisvan Erkal & Deborah Minehart, 2007. "Optimal Sharing Strategies in Dynamic Games of Research and Development," EAG Discussions Papers 200707, Department of Justice, Antitrust Division.
    3. Steinmetz, Alexander, 2010. "Competition, innovation, and the effect of knowledge accumulation," W.E.P. - Würzburg Economic Papers 81, University of Würzburg, Department of Economics.
    4. Fabiano Schivardi & Martin Schneider, 2008. "Strategic Experimentation and Disruptive Technological Change," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(2), pages 386-412, April.
    5. Alexander Steinmetz, 2015. "Competition, innovation, and the effect of R&D knowledge," Journal of Economics, Springer, vol. 115(3), pages 199-230, July.
    6. Ron N. Borkovsky, 2017. "The timing of version releases: A dynamic duopoly model," Quantitative Marketing and Economics (QME), Springer, vol. 15(3), pages 187-239, September.
    7. Dou, Winston Wei & Ji, Yan & Wu, Wei, 2021. "Competition, profitability, and discount rates," Journal of Financial Economics, Elsevier, vol. 140(2), pages 582-620.
    8. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, Centre for Economic Policy Research.
    9. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    10. David Besanko & Ulrich Doraszelski, 2005. "Learning-by-Doing, Organizational Forgetting, and Industry Dynanmics," Computing in Economics and Finance 2005 236, Society for Computational Economics.
    11. Dalida Kadyrzhanova, 2005. "Predatory Governance," Computing in Economics and Finance 2005 421, Society for Computational Economics.
    12. Luís Cabral, 2011. "Dynamic Price Competition with Network Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 83-111.
    13. Nisvan Erkal & Deborah Minehart, 2013. "Optimal Sharing Strategies in Dynamic," Department of Economics - Working Papers Series 1174, The University of Melbourne.
    14. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2007. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," Levine's Bibliography 321307000000000903, UCLA Department of Economics.
    15. Cabral, Luis M. B., 2002. "Increasing Dominance with No Efficiency Effect," Journal of Economic Theory, Elsevier, vol. 102(2), pages 471-479, February.
    16. Bayer, Christian, 2007. "Investment timing and predatory behavior in a duopoly with endogenous exit," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3069-3109, September.
    17. Z. Eddie Ning & J. Miguel Villas-Boas, 2022. "Following the Customers: Dynamic Competitive Repositioning," Management Science, INFORMS, vol. 68(2), pages 1002-1018, February.
    18. Christian Bayer, 2004. "The Other Side of Limited Liability: Predatory Behavior and Investment Timing," Industrial Organization 0407001, University Library of Munich, Germany.
    19. Christian Ewerhart & Julian Teichgräber, 2019. "Multi-battle contests, finite automata, and the tug-of-war," ECON - Working Papers 318, Department of Economics - University of Zurich.
    20. Colla, Paolo & Garcia, Filomena, 2016. "Technology adoption: Hysteresis and absence of lock-in," Economics Letters, Elsevier, vol. 141(C), pages 107-111.

    More about this item

    Keywords

    ;
    ;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General

    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:cpr:ceprdp:4249. See general information about how to correct material in RePEc.

    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: CEPR (email available below). General contact details of provider: https://cepr.org/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.