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

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  • Anderson, Axel
  • Cabral, Luís M B

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

  • Anderson, Axel & Cabral, Luís M B, 2004. "Go For Broke or Play it Safe? Dynamic Competition with Choice of Variance," CEPR Discussion Papers 4249, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:4249
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    Cited by:

    1. Mueller-Langer Frank & Andreoli-Versbach Patrick, 2017. "Leading-Effect, Risk-Taking and Sabotage in Two-Stage Tournaments: Evidence from a Natural Experiment," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 237(1), pages 1-28, February.
    2. Chen, Yongmin & Pan, Shiyuan & Zhang, Tianle, 2016. "Patentability, R&D direction, and cumulative innovation," MPRA Paper 73180, University Library of Munich, Germany.
    3. Thomas J. Holmes & David K. Levine & James A. Schmitz, 2012. "Monopoly and the Incentive to Innovate When Adoption Involves Switchover Disruptions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(3), pages 1-33, August.
    4. 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.
    5. repec:kap:revind:v:51:y:2017:i:1:d:10.1007_s11151-016-9542-z is not listed on IDEAS
    6. Troya-Martinez, Marta, 2016. "Vagueness and information-sharing," Games and Economic Behavior, Elsevier, vol. 100(C), pages 301-320.
    7. Kevin J. Boudreau, 2018. "Amateurs Crowds & Professional Entrepreneurs as Platform Complementors," NBER Working Papers 24512, National Bureau of Economic Research, Inc.
    8. Seel, Christian & Strack, Philipp, 2012. "Continuois Time Contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 376, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    9. Christos Genakos & Mario Pagliero, 2012. "Interim Rank, Risk Taking, and Performance in Dynamic Tournaments," Journal of Political Economy, University of Chicago Press, vol. 120(4), pages 782-813.
    10. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
    11. Genakos, Christos & Pagliero, Mario, 2009. "Risk taking and performance in multistage tournaments: evidence from weightlifting competitions," LSE Research Online Documents on Economics 28599, London School of Economics and Political Science, LSE Library.
    12. Chia-Ying Chan & Christine W. Lai & Liang-Chung Lee, 2017. "Strategic Choice of Risk: Evidence from Mutual Fund Families," Journal of Financial Services Research, Springer;Western Finance Association, vol. 51(1), pages 125-163, February.
    13. Mercedes Teruel & Agustí Segarra, 2011. "Productivity and R&D sources in manufacturing and service firms in Catalonia: a regional approach," ERSA conference papers ersa11p1860, European Regional Science Association.

    More about this item

    Keywords

    differential games; r&d competition;

    JEL classification:

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

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