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.

► This paper considers a static, single-period cooperative advertising model introduced and studied in several published papers.
► We realized that the model lacks constraints to guarantee that the sales function will be non-negative for all decision variables’ values.
► We fixed this problem and showed that almost all of our qualitative and qualitative results differ from the ones obtained in the previous papers.