An approach based on dynamic conjectural variations is advanced for developing dynamic advertising strategies in a Lanchester oligopoly differential game. The approach allows competitors to anticipate rival reactions to market-share state variables, and maintains the computational advantage of open-loop Nash equilibrium strategies. In an empirical application to the ready-to-eat cereal industry, it is shown that advertising strategies based on dynamic conjectural variations can better explain the advertising of the cereal competitors than can open- loop advertising strategies.

Closed-loop (perfect) equilibria in a Lanchester duopoly differential game of advertising competition are used as the basis for empirical investigation. Two systems of simultaneous nonlinear equations are formed, one from a general Lanchester model and one from a constrained model. Two empirical applications are conducted. In one involving Coca-Cola and Pepsi-Cola, a formal statistical testing procedure is used to detect whether closed-loop equilibrium advertising strategies are used by the competitors rather than open-loop strategies. In the second application, involving Anheuser-Busch and Miller, the general model is estimated. Results indicate that closed-loop equilibria better explain dynamic advertising competition than do open-loop equilibria. Also, closed-loop equilibrium advertising strategies implied by model estimates show that competitive advertising levels may or may not be monotonic in market share.