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

25 Pages Posted: 5 Mar 2004

See all articles by Axel Anderson

Axel Anderson

Georgetown University - Department of Economics

Luis M. B. Cabral

New York University (NYU) - Leonard N. Stern School of Business - Department of Economics; Centre for Economic Policy Research (CEPR)

Date Written: February 2004

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'.

Keywords: R&D competition, differential games

JEL Classification: C70, L10

Suggested Citation

Anderson, Axel and Cabral, Luis M. B., Go for Broke or Play it Safe? Dynamic Competition with Choice of Variance (February 2004). CEPR Discussion Paper No. 4249. Available at SSRN: https://ssrn.com/abstract=511123

Axel Anderson

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States

Luis M. B. Cabral (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business - Department of Economics ( email )

269 Mercer Street
New York, NY 10003
United States
212-998-0858 (Phone)
212-998-4218 (Fax)

HOME PAGE: http://www.stern.nyu.edu/~lcabral

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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