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Go for broke or play it safe? Dynamic competition with choice of variance

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  • Axel Anderson
  • Luís M. B. Cabral

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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  • Axel Anderson & Luís M. B. Cabral, 2007. "Go for broke or play it safe? Dynamic competition with choice of variance," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 593-609, September.
    • Handle: RePEc:bla:randje:v:38:y:2007:i:3:p:593-609
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    File URL: http://hdl.handle.net/10.1111/j.0741-6261.2007.00102.x
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    15. 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.
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    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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