Momentum in dynamic contests

We consider a two-player advertising race subject to momentum. Momentum is modeled as a complementarity between current and past campaign spending in a way that is reminiscent of models of addiction and habit formation: the more effective a player's past spending has been, the more effective her future spending will be. For symmetric races in which the effectiveness of spending is of the Cobb-Douglas form, we derive analytic solutions for the equilibrium path. Our theory rationalizes alternative campaign strategies including aggressive openings and the development of a warchest for a final campaign assault.