Dynamic conjectural variations in a Lanchester oligopoly

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 computional 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.