Working Paper: CEPR ID: DP4249
Authors: Axel Anderson; Lus M B Cabral
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
JEL Codes: C70; L10
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| players' relative positions (qi - qj) (C72) | choice of variance (R&D strategies) (O30) |
| leading player (higher qi) (L15) | chooses low variance (safe strategies) (G11) |
| lagging player (lower qi) (C73) | chooses high variance (riskier strategies) (G11) |
| players close in position (x is near zero) (C73) | choose risky strategies (D80) |