On a cooperative advertising model for a supply chain with one manufacturer and one retailer

Huang and Li (2001), Huang et al. (2002), Li et al. (2002), Xie and Ai (2006) and Yue et al. (2006) recently studied a game-theoretic model for cooperative advertising in a supply chain consisting of one manufacturer and one retailer. However, the sales-volume (demand) function considered in this model can become negative for some values of the decision variables, and in fact, this does happen for the proposed Stackelberg and Nash equilibrium solutions. Yue et al. (2006) acknowledge the negativity problem and suggest two constraints to fix it; however, they do not incorporate these constraints into their mathematical analysis. In this paper, we show that the results obtained by analyzing the advertising model under the constraints suggested by Yue et al. can differ significantly from those obtained in the previous papers. (C) 2011 Elsevier B.V. All rights reserved.