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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’.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 4249.

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Date of creation: Feb 2004
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Handle: RePEc:cpr:ceprdp:4249

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Keywords: differential games; r&d competition;

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References

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  1. Cabral, L., 2000. "Increasing Dominance with No Efficiency Effect," New York University, Leonard N. Stern School Finance Department Working Paper Seires 00-06, New York University, Leonard N. Stern School of Business-.
  2. 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.
  3. 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).
  4. Luis M.B. Cabral & Michael Riordan, 1992. "The Learning Curve, Market Dominance and Predatory Pricing," Papers 0039, Boston University - Industry Studies Programme.
  5. Dirk Bergemann & Juuso Valimaki, 2000. "Entry and Vertical Differentiation," Cowles Foundation Discussion Papers 1277, Cowles Foundation for Research in Economics, Yale University.
  6. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  7. Christopher Harris, 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 0044, Boston University - Industry Studies Programme.
  8. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  9. Budd, Christopher & Harris, Christopher & Vickers, John, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 543-73, July.
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Cited by:
  1. Seel, Christian & Strack, Philipp, 2012. "Gambling in Contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  2. Thomas J. Holmes & David K. Levine & James A. Schmitz, Jr., 2008. "Monopoly and the Incentive to Innovate When Adoption Involves Switchover Disruptions," NBER Working Papers 13864, National Bureau of Economic Research, Inc.
  3. Christos Genakos & Mario Pagliero, 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.
  4. Liad Wagman & Vincent Conitzer, 2012. "Choosing fair lotteries to defeat the competition," International Journal of Game Theory, Springer, vol. 41(1), pages 91-129, February.
  5. 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.
  6. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
  7. 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.
  8. 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.

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