Dynamic promotional budgeting and media allocation

This paper addresses the managerial problem of promotional budgeting and media allocation in a dynamic competitive framework. We develop an extended Lanchester model that is able to analyze multi-instrument promotion in an oligopoly. The competitors, each with a different initial position as well as economic value of the market share and communication effectiveness, adopt the strategy of maximizing their net present value of discounted profits, taking the other players' actions into account. The resulting differential game is solved using a novel method, providing both the open-loop strategy and the closed-loop strategy for each firm. We prove that our solution is a global Nash equilibrium. We develop a simple formula, that, when applied to an open-loop strategy, readily generates a feedback strategy. We also show that for both open- and closed-loop strategies, the proportion of the budget allocated to each instrument is invariant with time and depends only on instrument effectiveness. We illustrate the results and provide several managerial rules and discuss their application in practice. Finally, we show that our model favorably compares with other model in the literature in explaining actual data.