یادداشتی بر "تبلیغات تعاونی، نظریه بازی و زنجیره تامین تولید کننده - خرده فروش"

This note extends the results in the manufacturer-dominated game model of the paper by Li et al. (Omega 30 (2002) 347) to the case where the manufacturer's marginal profit is not large enough. In such situations, the profit of the entire supply chain under the co-op advertising mode is higher than the one under the Stackelberg game, which is consistent with the results of the original paper. However, the advertising expenditures of the manufacturer and the retailer under the co-op advertising model are not always larger than those under the Stackelberg game, which is different from the results of the original paper. Furthermore, the results are also compared with the simultaneous move game of the paper by Huang and Li (Eur. J. Oper. Res. 135 (2001) 527). The manufacturer always prefers the leader–follower structure rather than the simultaneous move structure, which is consistent with the results of the original paper. However, the retailer always prefers the simultaneous move structure rather than the leader–follower structure, which differs from the results of the original paper.

A recent paper by Li et al. [1] develops three strategic models for determining equilibrium marketing and investment effort levels for a manufacturer and a retailer in a two-member supply chain. The first model offers a formal normative approach for analyzing the traditional cooperative (co-op) advertising program where the manufacturer is the leader and the retailer is a follower. The second model provides a further analysis on this manufacturer-dominated relationship, by making use of the concept of “higher order Stackelberg equilibrium”. The third model incorporates the recent market trend of retailing power shifts from manufacturers to retailers to analyze efficiencies of co-op advertising programs. The first and the third models can also be found in other two papers by the same set of authors [2] and [3], while Ref. [2] presents discussions on another model where the manufacturer and the retailer simultaneously and noncooperatively maximize their own profits with respect to any possible strategies set by the other member in the system. All the discussions in Refs. [1], [2] and [3] for the sequential move Stackelberg game (the first model mentioned above) are based on a primary assumption of ρm/ρr⩾γ+1ρm/ρr⩾γ+1, and the part of ρm/ρr<γ+1ρm/ρr<γ+1 is missing. (Here ρmρm and ρrρr are the marginal profits for the manufacturer and the retailer, respectively, and γγ is the quasi-advertising elasticity [3] related to the one-period sales response volume function.) In the leader–follower structure, it is assumed that the manufacturer as the leader holds the extreme power and has almost complete control over the retailer, thus it seems reasonable to assume that the manufacturer's marginal profit is higher than the retailer's, and that is why ρm/ρr⩾γ+1ρm/ρr⩾γ+1 is implicitly assumed in Refs. [1], [2] and [3]. However, in recent severely competitive market, the marginal profits for both the manufacturer and the retailer tend to be low, thus the situations where the manufacturer's marginal profit is smaller than the retailer's are also possible. Even for the situations where the manufacturer's marginal profit is higher than the retailer's, the manufacturer's marginal profit may not be large enough to make the inequality ρm/ρr⩾γ+1ρm/ρr⩾γ+1 hold.

This research has been supported by NSFC Project 70471008. Thanks are also due to the anonymous referees for their helpful comments.