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

Axel Anderson and Luis M B Cabral ()

No 4249, CEPR Discussion Papers from C.E.P.R. Discussion Papers

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: differential games; r&d competition (search for similar items in EconPapers)
JEL-codes: C70 L10 (search for similar items in EconPapers)
Date: 2004-02
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