Game Analysis in a Dual Channels System with Different Power Structures and Service Provision

1 Introduction

With the popularity of information technology, in addition to selling products through traditional retailers, many brand name manufacturers, including Dell, Nike, and Apple, have introduced online channels to sell products to customers directly. The manufacturer can use such a dual channels system to attract the customers with different needs, which can increase its profits and help it be more competitive. However, the presence of online direct channel can result in fiercer competition between the manufacturer and the retailer. In order to win more consumers, the retailer will provide the additional service. In the meanwhile, dual-channel supply chain members’ different bargaining power can lead to different types of competition. A question therefore arises as to which type of game is the best for the manufacturer, the retailer and customers respectively in the dual-channel supply chain with channel price and the retail service competition? Our research is closely related to studies of dual-channel supply chain with price and service competition.

Indeed, there has been a large volume of research focused on channel selection and competition. Swaminathan and Tayur[1] focused on supply chain issues with the prevalence of e-commerce, and discussed the contributions of relevant analytical research models. Chiang, Chhajed and Hess[2] showed that direct channel can profit the manufacturer and may not always be detrimental to the retailer. Similarly, Cattani et al.[3] analyzed pricing strategies for a manufacturer that might mitigate the channel conflict. Furthermore, Chiang and Monahan[4] applied one-for-one inventory control policy, defined a cost structure in a dual-channel inventory model with stochastic demand for two consumer segments, and concluded that the dual-channel strategy outperforms the retail-only and direct-only strategies. Arya, Mittendorf and Sappington[5] demonstrated that encroachment can lower the wholesale price, which can mitigate double marginalization problems and secure Pareto improvements. Furthermore, Arya, Mittendorf and Yoon[6] demonstrated that a manufacturer can benefit from decentralized arrangements by imposing transfer prices above marginal cost. Hua, Wang and Cheng[7] examined how delivery lead time influences the manufacturer’s and retailer’s pricing decisions. Liu and Zhang[8] studied how entry into a direct distribution channel affects the manufacturer’s and retailer’s profits, and the retailer would embrace personalized pricing to deter the manufacturer from selling direct. Yan[9] developed a game theory model which can help the multi-channel company determine the optimal pricing strategy. Park and Keh[10] used game theory to look at the firm’s marketing decision variables when hybrid channels exist.

Goal differences between channel members will lead to channel conflicts. Therefore, collaboration and coordination in the dual-channel supply chain has attracted much attention in the past few years. Kurata, Yao and Liu[11] assessed supply chain coordination, and found that combining markup and markdown prices appropriately can coordinate supply chain and achieve a win-win outcome for each channel. Bernstein, Chen and Federgruen[12] identified a condition under which perfect coordination of two-echelon supply chains with a single supplier and a network of retailers via simple schemes can be achieved. In order to adjust the manufacturer-reseller relationship, Tsay and Agrawal[13] examined some ways including changes in wholesale pricing and paying the reseller a commission. Chen, Zhang and Sun[14] illustrated how the coordination schemes can coordinate the dual-channel supply chain and achieve a win-win outcome for each member. Shin and Benton[15] investigated the impacts of environmental factors on the effectiveness of quantity discount-based inventory coordination policies between a buyer and a supplier. Cai[16] proposed the contract coordination policy which is mutually beneficial for the supplier and the retailer in the contract-implementing Pareto zone. Boyaci[17] stated that the presence of simultaneous vertical competition and horizontal competition can induce the channel inefficiencies, and designed an appealing two-part compensation-commission contract. Raju and Zhang[18] developed a channel model with a dominant retailer, and showed that a manufacturer can select either quantity discounts or a menu of two-part tariffs as a channel coordination mechanism.

In recent years, service has already become an important factor which affects consumers’ channel choice. In order to maintain customer loyalty and attract new customers, both direct online channels and traditional retail channels try to provide additional service which can induce customers to make purchase decisions. First, some scholars study service provided in electronic channels, for example, Bernstein, Song and Zheng[19] suggested a novel view that free riding may not produce a negative impact on supply chain performance, and examined how the free riding affects a manufacturer’s channel structure decision. Lin and Mahmassani[20] considered the logistical and distribution factors that influence the commercial viability of business operation models, and illustrated providing the high level of service delivered to customers leads to higher delivery costs. By considering time-dependent consumer demand, Hsu and Li[21] formulated the nonlinear mathematical programming model to optimize a delivery service strategy, and suggested that discriminating service strategy is a better strategy. Secondly, some scholars conduct the research about service provided in traditional retail channels, for example, Dumrongsiri et al.[22] built the dual channel supply chain in which consumers are sensitive to price and service qualities, and showed that an improvement in retailer’s service quality may bring more profits to the manufacturer and both parties may benefit from a larger range of consumer service sensitivity in the dual channel through numerical analysis. Yao and Liu[23] considered the price competition between e-tail and retail channel under the Bertrand and the Stackelberg settings, and examined how the retail services value and the marginal cost of retail services affect the equilibrium price. Similarly, Yan and Pei[24] stated that the manufacturer’s direct channel can result in the improved retail services, which could help the retailer obtain a higher sales volume and alleviate the channel conflict in a dual-channel competitive market. Mukhopadhyay, Yao and Yue[25] presented the model where the manufacturer acts as the leader and the retailer adds value to the product at a cost, and considered the case of incomplete information the manufacturer may have about the retailer’s value-adding cost. Thirdly, others focus on the manufacturer and the retailer providing service at the same time, for instance, Yrjola[26] thought that on the basis of the traditional grocery shop, electronic grocery shopping operators offer service, and the supply chain should be redesigned to support EGS. In order to improve the service efficiency, Xiao, Dan and Zhang[27] proposed the service-cooperation Stackelberg and Bertrand models in the dual-channel supply chain, and showed that the manufacturer’s and the retailer’s service cost have great effect on the channels’ pricing decision.

As can be seen from the above literature review, most dual-channel supply chain literature focus on the competition and coordination between the channels in which consumers are price sensitive or service sensitive, however, they seldom consider that different power of supply chain members can result in different types of competition. It is a pity that they could not make a general evaluation concerning the impact of different types of game on competition equilibrium results. Therefore, this paper will attempt to build three game models of Manufacturer Stackelberg, Retailer Stackelberg, Vertical Nash, and evaluate which type of game is the best for the manufacturer, the retailer and customers respectively in the dual-channel supply chain when channels are competing in price and the retail service.

2 Problem Description and Model Building

4 Retailer Stackelberg Game

The game sequence of Retailer Stackelberg is as follows: Firstly, the retailer decides the service level s_t in the traditional retail channel to maximize its own profits π_r, and then according to the service level set by the retailer, the manufacturer sets the channel price p to maximize its profits π_m. Next we are going to solve the optimal channel price and retail service through backwards induction method. Let the subscript R* denote equilibrium solutions under Retailer Stackelberg game.

The profit function for the manufacturer is as follows:

The first-order condition characterizing equilibrium price is

Since ∂2πm∂p2=−2<0, the manufacturer’s profit function given service is strictly concave in price. Solving for p from the above Equation (15), we obtain the equilibrium price for the manufacturer:

Similarly for the retailer, the profit function is as follows:

Plug Equation (16) into Equation (17), and differentiate with respect to service and equate it to zero. We obtain the following formula:

Since ∂2πr∂st2=−(2e+3b2)<0, the retailer’s profit function is strictly concave in service.

Solving for s_t from the above Equation (18), we obtain the equilibrium service:

Plug Equation (19) into Equation (16), and we obtain the equilibrium price:

The corresponding traditional retail and direct channel demand quantities at the equilibrium price and service are respectively:

The corresponding retailer’s and manufacturer’s profits at the equilibrium price and service are respectively:

5 Vertical Nash Game

If the manufacturer and the retailer in a dual-supply chain have the same power, they conduct a Vertical Nash game. The sequence of Vertical Nash game is: The manufacturer decides the channel price p to maximize its own profits π_m; at the same time, the retailer decides the service s_t to maximize its own profits π_τ. Let the subscript N* denote equilibrium solutions under Vertical Nash game.

The profit function for the manufacturer is as follows:

The first-order condition characterizing equilibrium price is:

Since ∂2πm∂p2=−2<0, the manufacturer’s profit function given service is strictly concave in price, and the manufacturer can achieve maximum profits.

Similarly for the retailer, the profit function is as follows:

The first-order condition characterizing equilibrium service is

Since ∂2πr∂st2=−e<0, the retailer’s profit function is strictly concave in service, and the retailer can achieve maximum profits. Solving for p and s_t from Equation (26) and Equation (28), we obtain the equilibrium price and service:

The corresponding traditional retail and direct channel demand quantities at the equilibrium price and service are respectively:

The corresponding retailer’s and manufacturer’s profits at the equilibrium price and service are respectively:

6 Equilibrium Analysis with Different Power Structures

We have obtained equilibrium results in three competition scenarios in last section, and this part will contrast the dual-channel supply chain competition results above.

7 Conclusion

Different from the previous literature, this paper considers power structure into a dual channels system which consists of a manufacturer and a retailer facing common end consumers who are sensitive to both the channel price and retail service. Additionally, we develop three possible game scenarios, namely, Manufacturer Stackelberg, Retailer Stackelberg and Vertical Nash respectively. Furthermore, we derive equilibrium expressions for channel price, retail service level, demand quantity and supply chain members’ profits, and then contrast the results under three competition settings, which can give insights on which power structure is the most beneficial for the manufacturer, the retailer and customers.

The results show that consumers can get more benefits when supply chain members have equal power, which means that customers can receive higher retail service at the expense of lower price. A counterintuitive result shows that the retailer as a Stackelberg leader enjoys first-mover advantages in the decision making process, yet the manufacturer is more willing to act as a Stackelberg follower. Furthermore, Manufacturer Stackelberg and Vertical Nash is a strictly dominated strategy of the retailer and the manufacturer respectively. These above findings we get by applying a game theoretic concept into the dual-channel supply chain can fill the theoretical gap and serve as the foundation for the future empirical research.

While this paper provides the basis for future research on power structures in a dual channels system with service provision, there are limitations in our analysis. First, we assume a deterministic demand function that is linear in channel price and retail service variables in this paper, however, firms in supply chain are often facing uncertain demand, and hence further examination of the stochastic demand functions can gain more meaningful managerial insights. Second, the paper assumes the manufacturer and retailer are fully rational decision makers who possess complete information, but some information might be incomplete to them. Therefore, we can explore competition equilibriums under incomplete information setting.