DP4249 Go For Broke or Play it Safe? Dynamic Competition with Choice of Variance

Author(s):	Axel Anderson, Luís M B Cabral
Publication Date:	February 2004
Keyword(s):	differential games, r&d competition
JEL(s):	C70, L10
Programme Areas:	Industrial Organization
Link to this Page:	cepr.org/active/publications/discussion_papers/dp.php?dpno=4249

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?.