تبلیغات تعاونی، نظریه بازی و زنجیره تامین تولید کننده ـ خرده فروش

Cooperative (co-op) advertising plays a significant role in marketing programs in conventional supply chains and makes up the majority of promotional budgets in many product lines for both manufacturers and retailers. We develop three strategic models for determining equilibrium marketing and investment effort levels for a manufacturer and a retailer in a two-member supply chain. Especially, we address the impact of brand name investments, local advertising, and sharing policy on co-op advertising programs in these models. The first model offers a formal normative approach for analyzing the traditional 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. The third model incorporates the recent market trend of retailing power shifts from manufacturers to retailers to analyze efficiencies of co-op advertising programs. We examine the effect of supply chain on the differences in profits resulting from following coordinated strategies as opposed to leader–follower strategies. A cooperative bargaining approach is utilized for determine the best co-op advertising scheme for achieving full coordination in the supply chain.

In the recent years, several papers dealt with vertical cooperative advertising in a manufacturer–retailer channel (for the sake of simplicity, we refer to cooperative advertising in the following). This type of collaboration can be defined as an financial agreement, in which the manufacturer offers to bear either a certain part or the entire advertising expenditures of his retailer (Bergen and John, 1997). Thereby, he intends to increase the retailer’s advertising, which has the task to stimulate the immediate demand of the customers. With this financial assistance, the retailer can increase his level of advertising, which leads to higher sales for both, the retailer and the manufacturer (Somers et al., 1990). Though being a significant part of many manufacturers’ advertising budgets (for example, a total sum of $15 billion was invested in such programs in the United States in 2000), most firms seem to determine the participation rate arbitrarily and without detailed analysis on 50% or 100% (Nagler, 2006). The research on cooperative advertising can be roughly divided into two groups. Authors belonging to the first group concentrate their analysis solely on advertising. The first mathematical modeling of cooperative advertising was the work of Berger (1972), who proposed a financing of the retailer’s advertising expenditures by a discount on the wholesale price. Dant and Berger (1996) adopted this approach to the context of franchising. Karray and Zaccour (2006) considered a bilateral duopoly and demonstrated, that cooperative advertising can also have harmful impacts on the retailers. In contrast to the latter examples, which are based on static models, Jørgensen et al., 2000, Jørgensen et al., 2003 and Jørgensen and Zaccour, 2003 studied the effects of cooperative advertising in a dynamic environment by using a goodwill function, on which the retailer’s advertising has either positive or negative effects. The first one comparing different types of manufacturer–retailer relationships by game theory was the work of Huang and Li (2001), who used a demand function which depends both on the local advertising expenditures of the retailer and on the global advertising expenditures of the manufacturer. Though emphasizing the changed power structure in favor of the retailers, they considered equal power distribution (Nash equilibrium), manufacturer-leadership (Stackelberg manufacturer equilibrium) and the case were manufacturer and retailer act in cooperation and bargain for the division of profits. Similar approaches with slightly modified demand functions can be found in Li et al., 2002, Huang et al., 2002 and Huang and Li, 2005. Representatives of the second group, to which the present paper belongs to, also include other decision variables like pricing, as it can be found in Bergen and John, 1997, Kim and Staelin, 1999 and Karray and Zaccour, 2007. For instance, Yue et al. (2006) extended the model of Huang and Li (2001) by a price-sensitive component within the demand function in order to deliver the optimal advertising expenditures of both channel members as well as the optimal price discount offered to the costumers by the manufacturer. They compared the results of the Stackelberg manufacturer equilibrium to the cooperation. In lieu of the price discount, Szmerekovsky and Zhang (2009) included the resulting retail price in their demand function and calculated the Stackelberg manufacturer equilibrium. In contrast to the latter, the retailer fully determines the price demand, which previously was influenced only by the manufacturer. The model proposed by Xie and Wei (2009) is based upon a different demand function, which enabled the authors to handle the (cooperative) advertising and pricing decisions of both channel members contemporaneously. In this context, closed-form solutions of the Stackelberg manufacturer equilibrium and the cooperation were derived. Yan (2010) customized this model in order to fit to the e-marketing environment. The assumption of a dominant manufacturer is indeed very common in marketing literature, but the development of large retailers like Wal-Mart and, according to that, the shift of market power necessitates additional analyses. The first paper, which considered not only a leadership of the manufacturer, but also a dominant retailer, was written by Xie and Neyret (2009). Besides this Stackelberg retailer equilibrium, they calculated also the Nash equilibrium, the Stackelberg manufacturer equilibrium and the cooperation. The work of SeyedEsfahani et al. (2011) applied these four games on the model proposed by Xie and Wei (2009), but relaxed the assumption of a linear price demand function by introducing a new parameter ν which can cause either a convex (ν < 1), or a linear (ν = 1) or a concave (ν > 1) curve. Lastly, a recent paper of Kunter (2012) follows a different approach and concentrates on establishing channel coordination by means of a royalty payment contract. Table 1 summarizes the cooperative advertising models, which are most related to our approach, as well as the corresponding demand functions and games being used. Please note that both Xie and Neyret, 2009 and SeyedEsfahani et al., 2011 only initially used the parameters α and β within their price demand function and normalized them to one during further calculus.is clearly visible, that only the latter two really take into account the changed market structure, i.e. the shift of power from manufacturers to retailers, by including Nash and Stackelberg retailer equilibrium. However, both had to deal with some mathematical difficulties during the calculation of the manufacturer’s decision problem for these new games: Following the notation explained in Table 2, the profit functions of both articles can be written as In this paper, we intend to relax this restrictive assumption of identical margins to get better insights into the effects of market power on the distribution of channel profits. Through a modification of the profit functions, we are able to extend the existing research by unrestrained Nash and Stackelberg retailer equilibria. Thereby, we follow the modified price demand function introduced by SeyedEsfahani et al. (2011), as we expect more insights as from the linear function of Xie and Wei (2009). Contrary to the authors, we will not normalize the parameters α and β to one in order to be able to adapt the function to the real price demand. The remainder is organized as follows: In Section 2, we propose our modification of the profit functions and calculate the Nash (2.1), the Stackelberg manufacturer (2.2), the Stackelberg retailer equilibrium (2.3) and the cooperation (2.4). The latter game has to be complemented by a bargaining model, which is used to determine the profit split between manufacturer and retailer. Therefore, we introduce the asymmetric Nash bargaining model of Harsanyi and Selten, 1972 and Kalai, 1977 in Section 2.5. The results of these four games are compared in Section 3 via numerical examples. Section 4 summarizes our main findings and indicates possible directions of further research.

This paper addresses optimal pricing and advertising decisions in a manufacturer–retailer supply chain with consumer demand, that depends both on the retail price and on the channel members’ advertising expenditures. Additionally, a cooperative advertising program is considered, where the manufacturer can bear a certain fraction of the retailer’s advertising costs. By means of game theory, we analysed four different relationships within the supply chain: A non-cooperative behavior with equal distribution of power, two situations in which one player dominates his counterpart and a cooperation between manufacturer and retailer. We adopted a model recently published by SeyedEsfahani et al. (2011) and introduced the retailer margin m as a new decision variable. This customization of the original model enabled us to abandon the restrictive assumption of identical margins previously used both in Nash and in Stackelberg retailer equilibrium. Furthermore, our model extends also the work of Xie and Wei (2009), which is a special case with linear price demand (i.e. ν = 1). The main contributions of our research are as follows: (a) Without the assumption of identical margins, the profit split between manufacturer and retailer can be determined unrestricted and solely depending on the underlying set of parameters and game structure. Anyhow, we observed, that a Nash equilibrium leads to identical margins on its own, so that the assumption was justified in that case, but not in the Stackelberg retailer equilibrium. The numerical computations in Section 3 though showed, that our generalized model yields more differentiated results concerning the dominant game structure, which decision makers can use as recommendation for practical problems. (b) A generalization of the price demand function used in SeyedEsfahani et al. (2011) by introducing the parameters α and β. These parameters do not affect the structure of the results (i.e. the ratio between manufacturer’s and retailer’s profit), but exclusively the level of prices, advertising expenditures and profits. Therefore, these parameters can be used to adapt the proposed model more precisely to practical contexts. (c) The cooperation, which is characterized by the lowest retail price and the highest advertising expenditures, produces the highest total profit of all considered games. We showed the feasibility of a cooperation for moderate sets of parameters k and ν and exemplified the asymmetrical Nash bargaining model of Harsanyi and Selten, 1972 and Kalai, 1977, which allows to consider risk attitude and bargaining power contemporaneously. Future research could apply our approach of using the retailer margin as decision variable also to the model of Xie and Neyret (2009), which suffers from the assumption of identical margins in the Nash and Stackelberg retailer equilibrium, too. Moreover, the introduction of additional supply chain members would render possible to analyse not only the interaction between the two echelons, but also the competition between two manufacturers or retailers. The increased complexness could though necessitate the application of metaheuristics (see, e.g. Yu and Huang (2010) for a recent example). In multiple player framework, the forming of coalitions during bargaining seems to be another interesting field of research.