Optimal Control of an Oligopoly Model of Advertising

We examine an oligopoly model of advertising competition where each firm's market share depends on its own and its competitors’ advertising decisions. A differential game model is developed and used to derive the closed-loop Nash equilibrium under symmetric as well as asymmetric competition. We obtain explicit solutions under certain plausible conditions, and discuss the effects of an increase in the number of competing firms on advertising expenditure, market share and profitability.