Differential game approach to pricing and advertising decisions


This study proposes a model to make concurrent decisions on dynamic pricing and advertising to maximise firms' profitability over an infinite time horizon in a duopoly market. To this end, the Nerlove-Arrow pricing and advertising model is designed in the presence of shifting costs in a dynamic duopolistic competition as a differential game. The Nash equilibrium solution is defined based upon a set of Hamilton–Jacobi–Bellman. Four scenarios are applied for economic interpretations and the efficacy of the model.


The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.


Dynamic pricing, Dynamic advertising, Duopoly market, Shift costs, Differential game


Mahdiraji, M.A., Hatami-Marbini, A., Moazed, N.M., Ansari, M., Kamardi, A.A.A. (2021) Differential game approach to pricing and advertising decisions. Operations Research Letters, 49 (5), pp. 688-695


Research Institute

Centre for Enterprise and Innovation (CEI)