Stackelberg Games In Supply Chain Management

Game theory currently has become one of the essential tools to learn members’in-teractive optimization problems in Supply Chain Management (SCM). In a supply chain, members, such as manufacturers, distributers and retailers, typically play different roles in a game because of serving in different parts of the chnnel. When playing some games, the members in different parts may move sequentially. Generally, people term the first mover(s) as the leader(s) and the following mover(s) as the follower(s). A game in such a leader-follower environment is called a Stackelberg game in which the follower responds according to its observation of the leader’s action and the leader determines its optimal strategy subjecting to its anticipation of the follower’s coping strategy. So far, Stackel-berg games have been widely used in SCM studies, such as buyback contracts, quantity discount problems, channel configurations and cooperative advertising.In this dissertation, we employ Stackelberg games to study three new SCM topics:(1) return policies/buyback contracts in the presence of supply competition;(2) channel design for a three-tier supply chain in a dual-channel dual-sourcing perspective; and (3) operational principles of co-branding effort decision, cost allocation and partner selection.(1) Return policies/buyback contracts with competing suppliers:The classic study by Pasternack (1985) demonstrated that a channel with a supplier and a retailer that play a Stackelberg game can be coordinated by the manufacturer’s partial credit buyback con-tracts-allowing unlimited returns from the retailer and offering a partial credit for per returned unit. The recent article by Bandyopadhyay and Paul (2010)(BP) concluded that the full-credit return policies, which were considered suboptimal from the perspective of channel coordination, are prevalent in practice. BP searched for an explanation for the phenomenon that they termed the "Pasternack paradox" in a setting of a two-tier Stackel-berg game where two competing suppliers, game leaders, play a Nash subgame. They argued that the underlying reason is that the competition between suppliers rather than the coordination among channel members dominates business practice. However, both our theoretical proof and generated counterexample show that not only the proof but also the claimed results are actually wrong and thus the model in BP fails to explain the "Paster-nack paradox". To provide alternative explanations for the seemingly suboptimal business practice-"Pasternack paradox", we employ a Stackelberg game to examine buyback contracts from the perspective of manufacturers’competition. We first consider a setting where two manufacturers/suppliers sell distinct products to a retailer. The limited ordering ca-pacity (e.g., limited shelf space) of the retailer generates competition between the manu-facturers, who compete for retail resource through each offering the retailer a well-designed buyback contract. We demonstrate that in equilibrium the suppliers will offer full credit buyback contracts to the retailer. As a generalization, we further consider a set-ting with a single supplier and a retailer where, however, the retailer has a reservation for the minimum marginal return on its investment. We show that a full credit buyback con-tract remains the best choice for the supplier. Our findings provide an interpretation for empirical observations that full credit return policies rather than partial credit return poli-cies are widely adopted in practice. In a more general sense, we exemplify the need to re-examine the channel-coordinating contracts from a competitive view.(2) Channel design for a three-tier supply chain in the perspective of dual-channel dual-sourcing:We analyze a supply chain where a manufacturer distributes a product to a retailer through two suppliers (channels). Players are profit maximizing and play a three-stage Stackelberg game where the manufacturer acts as the game leader. The two suppli-ers, supplier1and2, differ in their ability of offering return credits; supplier1commits to return unsold products but supplier2does not. They play a Nash subgame through charging different wholesale prices from the retailer. For such three-tier supply chain, we first derive the retailer’s optimal ordering policy. Then, based on this, we establish the existence and uniqueness of the pricing Nash equilibrium for the two suppliers with uni-form demand distribution. Next, we solve the manufacturer’s optimal wholesale price that it charges from the two suppliers. The equilibrium suggests that the manufacturer’s pric-ing strategy as well as the two suppliers’competition for different segments of the market depend on the demand uncertainty heavily. Compared with a single-channel system, we analyze the motivation for the manufacturer (in a dual-channel perspective) to have such a channel configuration and the retailer (in a dual-sourcing perspective) to take such a sourcing policy. We surprisingly find that when demand uncertainty is relatively large (not too small and not extremely large), even if all players are self-interest maximizing, the introduction of a second channel may bring Pareto gains to all channel members; the improvement is derived from the manufacturer’s willingness to push a valid competition between two channels. More interestingly, even though the demand uncertainty is ex-tremely large, adding a second channel is still possible to benefit all players if the manu-facturer can properly set a non-self-interest-maximizing pricing policy. We also find that, perhaps counterintuitively, supplier1’s possessing strength in salvaging the unsold prod-uct does not necessarily bring disadvantage to supplier2in competition.(3) Operational principles of co-branding effort decision, cost allocation and partner selection:As a marketing tactic to ally two or more brands, co-branding has attracted considerable academic interest during the past two decades. Studies on related issues have mostly used empirical/experimental means to confirm various co-branding effects. Although several studies have analytically discussed the related decision problems, none has learned the participants’optimal branding effort level and the related cost allocation mechanism. We employ a Stackelberg differential game to model the self-branding and co-branding games between co-branding header and modifier. Our solution helps explain players’decision rules for optimal self-branding and co-branding efforts as well as co-branding cost allocation and partner selection. The equilibrium suggests that each play-er’s equilibrium self-branding effort is a feedback policy of its sales state, whereas the co-branding effort is independent of sales state. For co-branding cost allocation, we find that co-branding modifier may share a proportion of co-branding cost or, perhaps counterintu-itively, charges the head instead. For the players’ partner selection, we find that some in-consistent results reported by extant studies can be actually unified by our theoretical model. Finally, we compare our results with the self-branding-only and co-branding-only cases to better understand the relationship between self-branding and co-branding.The Stackelberg games developed in our thesis are found to be able to cover the above three new topics and more importantly, succeed in explaining some interesting and important appeared phenomena, which have not been successfully explained before, and thus provide lots of valuable managerial insights for practical application in SCM.