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

  • Anderson, Axel
  • Cabral, Luís M B

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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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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  1. Christopher Harris, 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 0044, Boston University - Industry Studies Programme.
  2. Cabral, Luis M B & Riordan, Michael H, 1994. "The Learning Curve, Market Dominance, and Predatory Pricing," Econometrica, Econometric Society, vol. 62(5), pages 1115-40, September.
  3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, volume 1, number 5474.
  4. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  5. 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).
  6. 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.
  7. 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.
  8. Dirk Bergemann & Juuso Valimaki, 2000. "Entry and Vertical Differentiation," Cowles Foundation Discussion Papers 1277, Cowles Foundation for Research in Economics, Yale University.
  9. Luis Cabral, 2000. "Increasing Dominance With No Efficiency Effect," Working Papers 00-06, New York University, Leonard N. Stern School of Business, Department of Economics.
  10. 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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