Strategic Rivalry for Market Share: A Contest Theory Approach to Dynamic Advertising Competition

The paper extends the Lanchester model of advertising competition to a setup in which the rate at which a firm attracts customers from its competitors depends not only on the firm's own advertising effort, but also on the efforts of its rivals. Doing so enables us to use attraction rate specifications borrowed from the economic theory of contests. Exploiting the fact that the sum of attraction rates equals one, we show that the differential equations that define the evolution of market shares in the Lanchester model can be considerably simplified. This makes the optimization problems of the firms considerably easier to analyze. Finallly, to illustrate how the above extensions work, three alternative specifications of attraction rates are studied: the Tullock ratio formulation, a linear transformation of the Tullock ratio, and a specification that incorporates an exogenous bias.