Discussion paper

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

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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Citation

Cabral, L and A Anderson (2004), ‘DP4249 Go For Broke or Play it Safe? Dynamic Competition with Choice of Variance‘, CEPR Discussion Paper No. 4249. CEPR Press, Paris & London. https://cepr.org/publications/dp4249