The I Days of Christmas: A Model for Competitive Advertising Over An Intensive Campaign

During a pre-Christmas campaign in which daily sales are generally increasing, it is important to achieve a proper balance in advertising allocation between the final days of heavy sales and the earlier days of the campaign when sales are lighter but advertising might affect sales farther into the future. This paper presents a model of such a problem for two competing firms, an algorithm for solution of the model, numerical examples, and a proof of the algorithm.

An equilibrium solution is found in which each firm applies the same proportioning vector to distribute its total advertising budget over the N days.