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): r&d competition , differential games

JEL(s): C70 , L10

Programme Areas: Industrial Organization

Link to this Page: www.cepr.org/pubs/dps/DP4249.asp

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’.