Cooperative Advertising and Pricing in a Dynamic Stochastic Supply Chain: Feedback Stackelberg Strategies

Cooperative (co‐op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co‐op advertising policy, i.e., a participation rate that specifies the percentage of the retailer's advertising expenditure that it will provide. In addition, it also announces the wholesale price. In response, the retailer chooses its optimal advertising and pricing policies. We model this supply chain problem as a stochastic Stackelberg differential game whose dynamics follows Sethi's stochastic sales‐advertising model. We obtain the condition when offering co‐op advertising is optimal for the manufacturer. We provide in feedback form the optimal advertising and pricing policies for the manufacturer and the retailer. We contrast the results with the advertising and price decisions of the vertically integrated channel, and suggest a method for coordinating the channel.     

面向网络零售平台的合作广告策略研究

制造商通过第三方网络零售平台开展直销渠道已经成为普遍模式。除价格策略外，广告宣传是企业获得消费者最常用的策略之一，已有研究表明，合作广告策略可有效协调供应链冲突和优化绩效，但在新零售模式中，传统渠道和网络渠道的特点使得网络零售平台和传统零售商的广告宣传对不同销售渠道的影响更加复杂和有趣，因此本文研究网络零售平台的参与对制造商合作广告策略的影响。在文中通过数学建模的方法比较制造商的四种不同策略：不合作策略、制造商仅与传统零售商合作的策略、制造商仅与网络零售平台合作的策略和制造商与两者均合作的策略，通过对不同策略中渠道成员的利润进行比较，可得以下结论：1）制造商的最佳策略为同时与传统零售商和网络零售平台合作；2）当两渠道的广告存在相互"搭便车"行为时，渠道成员之间最优策略一致；3）当网络、传统渠道的广告宣传为竞争关系时，渠道成员的最优策略不一致，但存在"相对"最优策略：传统零售商和网络零售平台同时与制造商合作，该策略下传统零售商、网络零售平台的利润可能会降低，但降低比例为最小。     

Co‐Op Advertising in Dynamic Retail Oligopolies

We study a supply chain in which a consumer goods manufacturer sells its product through a retailer. The retailer undertakes promotional expenditures, such as advertising, to increase sales and to compete against other retailer(s). The manufacturer supports the retailer’s promotional expenditure through a cooperative advertising program by reimbursing a portion (called the subsidy rate) of the retailer’s promotional expenditure. To determine the subsidy rate, we formulate a Stackelberg differential game between the manufacturer and the retailer, and a Nash differential subgame between the retailer and the competing retailer(s). We derive the optimal feedback promotional expenditures of the retailers and the optimal feedback subsidy rate of the manufacturer, and show how they are influenced by market parameters. An important finding is that the manufacturer should support its retailer only when a subsidy threshold is crossed. The impact of competition on this threshold is nonmonotone. Specifically, the manufacturer offers more support when its retailer competes with one other retailer but its support starts decreasing with the presence of additional retailers. In the case where the manufacturer sells through all retailers, we show under certain assumptions that it should support only one dominant retailer. We also describe how we can incorporate retail price competition into the model.     

基于供应链的合作促销与定价问题

本文针对供应链中厂商和销售商之间的合作促销问题,使用博弈论的方法主要就最优的合作促销费用投入和定价进行了研究。首先讨论了传统的厂商为领导者,销售商为跟随者的情形,接着考虑到如今销售商地位的提高,对此进行了拓展,讨论了销售商为领导者的情形。最后以前两种情形为参照,建立了厂商和销售商之间Pareto改进的合作促销模型,并利用Nash讨价还价和效用理论得出了Pareto改进情形下的最优结果。     

Differential Pricing for Information Sharing Under Competition

We consider a two‐echelon supply chain with a manufacturer supplying to multiple downstream retailers engaged in differentiated Cournot competition. Each retailer has private information about uncertain demand. The manufacturer is the Stackelberg leader who sets the contract terms with the retailers, and benefits from retailers sharing their private information. When all retailers are given the same wholesale price, truthful information sharing is not an equilibrium outcome. We propose two variants of differential pricing mechanisms that induce truthful information sharing by all retailers. The first variant rewards a retailer for providing optimistic information and achieves truthful information sharing as a unique equilibrium. The differential pricing mechanism is optimal in the class of linear‐price, incentive‐compatible, direct mechanisms. The second variant, which incorporates provision for a fixed payment in addition to wholesale prices, preserves all the equilibrium properties of the first variant and additionally “nearly coordinates” the supply chain. Our analysis of differential pricing with a fixed payment provides interesting observations regarding the relationship between product substitutability, number of retailers, information precision, and market power. As products become closer substitutes and/or number of retailers increase, the manufacturer's market power increases, enabling her to extract a larger fraction of the supply chain surplus.     

不同权力结构和联盟策略下风险规避型闭环供应链决策

本文旨在探讨不同渠道权力结构和联盟策略下风险规避型闭环供应链的决策问题。考虑到产品需求和废旧产品回收的不确定性及决策者的风险规避特性,在制造商主导、零售商主导及制造商和零售商势力均衡三种情形下,分别构建了制造商和零售商联盟与不联盟时的闭环供应链博弈模型,获得了六个博弈模型下的均衡解,对比分析了不同模型下产品定价、废旧产品的最优回收价格和供应链及其成员的期望收益。研究结果表明,在制造商和零售商不联盟的情形下,决策者的风险规避程度增加能够缓解双重边际效应,供应链期望收益与风险规避程度正相关,而在制造商和零售商联盟的情形下,供应链期望收益与风险规避程度负相关;制造商和零售商不联盟时,制造商和零售商势力均衡的渠道权力结构对消费者最有利,而制造商和零售商联盟时,制造商和零售商势力均衡的渠道权力结构对消费者最不利;制造商和零售商权力结构不对等时最优价格决策之间的关系与制造商和零售商的风险规避程度有关;供应链期望收益在制造商和零售商势力均衡下最大,制造商期望收益在制造商主导的渠道权力结构下最大,零售商期望收益在零售商主导的渠道权力结构下最大。     

零售商竞争下的垂直合作广告模型

关于合作广告问题的研究目前主要集中在探讨单一制造商和单一零售商时的情况。本文则在此基础上,把研究扩展到单一制造商和多个竞争性的零售商的情况。零售商的商品需求量除了受到自己的广告投入影响还受到竞争者广告投入的影响。在这种情况下,合作广告不同于单一零售商时的情况。那么在新的情形下,零售商的广告投入策略如何?制造商针对不同的零售商怎样制定补贴策略?哪些因素影响以及如何影响对不同营销渠道的选择?这些问题是本文的主要研究内容。     

Advertising in Asymmetric Competing Supply Chains

Advertising is a crucial tool for demand creation and market expansion. When a manufacturer uses a retailer as a channel for reaching end customers, the advertising strategy takes on an additional dimension: which party will perform the advertising to end customers. Cost sharing (“co‐operative advertising”) arrangements proliferate the option by decoupling the execution of the advertising from its funding. We examine the efficacy of cost sharing in a model of two competing manufacturer–retailer supply chains who sell partially substitutable products that may differ in market size. Some counterintuitive findings suggest that the firms performing the advertising would rather bear the costs entirely if this protects their unit profit margin. We also evaluate the implications of advertising strategy for overall supply chain efficiency and consumer welfare.     

Manufacturer encroachment with advertising

This paper studies manufacturer encroachment in a supply chain wherein the manufacturer and/or the retailer should invest in informative advertising. Using a game-theoretic framework, we explore three schemes of advertising and their influences on manufacturer encroachment. First, if the manufacturer controls advertising, encroachment will result in higher advertising intensity relative to the non-encroachment case, sometimes leading to a win-win situation for both the manufacturer and the retailer as the boosted demand flows into the wholesale market under encroachment. Second, if the retailer controls advertising, an encroaching manufacturer should further reduce the wholesale price as compared to the counterpart with no advertising. This downward pressure on wholesale price can benefit the retailer, but might hurt the encroaching manufacturer. Third, we incorporate manufacturer advertising and retailer advertising into a cooperative advertising scheme, where the manufacturer can set a participation rate to adjust the advertising cost for the retailer. Interestingly, an encroaching manufacturer will pay the retailer more to subsidize his advertising cost. Under this scheme, the manufacturer is always better off under encroachment, and the retailer can also gain as a result of advertising cost-sharing from the manufacturer. Our results also apply to the case of persuasive advertising. Although persuasive advertising leads to different prices or advertising decisions, there are always chances for the retailer to benefit from manufacturer encroachment.     

双渠道零售商和传统零售商的定价策略

在单制造商和两个具有竞争行为零售商的供应链系统中，本文研究了双渠道零售商和传统零售商的定价决策问题。首先，在零售商间进行Stackelberg博弈假设前提下，分别针对双渠道零售商和传统零售商作为领导者的情况，构建了两种模式下的零售商定价决策模型，给出了零售商的最优定价策略；其次，分析了零售商在特定情形下的定价策略；最后，用数值算例分析了模型参数对最优结果的影响。通过对比研究和数值算例分析发现：对于零售商来说，作为Stackelberg的领导者时的总利润要比作为追随者时的总利润大；对于供应商而言，传统渠道的零售商做主导者时的总利润要比双渠道零售商做主导者时的总利润大。     

不同渠道权力结构和信息结构下供应链定价和销售努力决策

本文针对零售商销售努力和销售价格影响需求情况下的制造商-零售商两级供应链,研究不同渠道权力结构和信息结构下供应链的分散决策。基于博弈理论和建模方法,对几种权力结构和信息结构情景建立相应模型,通过理论与数值分析对不同博弈均衡进行比较。研究表明,随着零售商势力逐步增强制造商利润会逐步恶化;但零售商势力增强能否带来更多利润,取决于需求对价格和销售努力的敏感度、销售努力成本以及信息结构。占优一方可以通过获取对方更多信息来改善自己处境。若占优零售商不得不依赖于对制造商成本先验分布进行决策,当估计的均值大于真实成本时,适度的方差对零售商更有利。最后,讨论了销售努力成本分担的合作机制,针对非合作博弈给出了帕累托改进的合约区间和 Nash讨价还价均衡。     

Controlling Power Retailer's Gray Activities Through Contract Design

We develop a model that captures dynamic relationships of a supply chain populated by a dominant retailer and a number of fringe retailers. The two types of retailers are asymmetric in buying power, retailing cost, and the ability to service the manufacturer's product. The wholesale prices offered through a quantity discount (QD) schedule can coordinate such a supply chain, but invite channel flow diversion type of gray trading between the dominant retailer and the fringe retailers. Our analysis is focused on how such a channel can be coordinated and the gray market activities be prevented. We propose a dynamic QD contract or a revenue‐sharing contract that the manufacturer can use to fight the gray market activity. The performance of the supply chain and the manufacturer's profit under each of the two contract forms are compared and managerial guidelines are provided to help the manufacturer make a judicious choice.     

网络外部性对双渠道供应链信息分享的影响

研究了网络外部性对双渠道供应链信息分享的影响。分别建立了存在网络外部性和不存在网络外部性下的双渠道供应链模型,通过比较零售商信息分享和不分享下其与制造商的期望利润。研究发现：当未考虑产品的网络外部性时,零售商不与制造商分享其市场需求信息,与已有研究一致。当考虑了产品网络外部性且网络外部性较小时,零售商仍不与制造商分享市场需求信息;然而,当网络外部性较大时,零售商与制造商分享其市场需求信息。此外,零售商与制造商共享其市场需求信息有助于增加制造商和供应链利润。     

不完全信息下再制造逆向供应链的定价与协调研究

本文探讨了回收量随机情况下的单一制造商和两个零售商组成的再制造逆向供应链系统的定价策略。在完全信息下,分别得到了Stackelberg博弈和联合博弈下的可行策略集合及可行解。在不完全信息下,运用信号甄别方法及激励相容约束得到了两个最优定价合同。研究表明:定价合同可以有效避免逆向选择问题,保证回收市场的稳定性;通过签订合同,制造商和零售商的利润均有所增加;制造商可通过零售商的履约表现控制其回收量,并对未完成任务的零售商进行惩罚;高运营成本零售商会不断降低运营成本以增加利润。     

Online Manufacturer Referral to Heterogeneous Retailers

Since the development of the Internet, thousands of manufacturers have been referring consumers visiting their websites to some or all of their retailers. Through a model with one manufacturer and two heterogeneous retailers, we investigate whether it is an equilibrium for the manufacturer to refer consumers exclusively to a retailer or nonexclusively to both retailers. Our analysis indicates that nonexclusive referral is the manufacturer's equilibrium choice if the referral segment market size is sufficiently large; otherwise, exclusive referral is the equilibrium choice. In exclusive referral, the manufacturer would refer consumers to the more cost‐efficient and smaller retailer. In the presence of infomediary referral, it is less likely for both exclusive and nonexclusive referrals to be an equilibrium, as the infomediary referral segment grows. We also show our qualitative results are robust even if there were price discrimination among consumers, referral position disparity, local consumers, and asymmetric referral market sizes.     

Impacts of demand uncertainty on retailer's dominance and manufacturer-retailer supply chain cooperation

Recent studies in marketing and distribution channels have shown that the balance of power between manufacturers and retailers is shifting. Based on this observation, we investigate a two-echelon supply chain with a manufacturer and a retailer in this paper. We first develop retailer-dominant non-cooperative game models by introducing a sensitivity of retailer's order quantity to manufacturer's wholesale price; then we analyze two cooperative scenarios, in which the Nash bargaining model is utilized to implement profit sharing between the manufacturer and the retailer. Under the assumption that the manufacturer and the retailer are risk-neutral, we find that the manufacturer and the retailer can bargain to cooperate at any level of retail-market demand uncertainty with exogenous retail price. However, the cooperation is conditional on retail-market demand uncertainty with endogenous retail price: it can be implemented if the fluctuation of retail-market demand is relatively small, and the measure of retail-market demand uncertainty does not exceed an upper bound. Theoretical and numerical analyses show that the retailer's dominance over the manufacturer increases with the increase in the sensitivity of retailer's order quantity to manufacturer's wholesale price under a limitation of retail-market demand uncertainty. Numerical analyses also show that the retailer's dominance decreases with the increase in retail-market demand uncertainty.     

Optimal Pricing and Rebate Strategies in a Two‐Level Supply Chain

For many product categories, manufacturers and retailers often offer rebates to stimulate sales. Due to certain adverse effects, however, some manufacturers and retailers are contemplating the elimination of their rebate programs. This paper sheds light on the debate about the value of rebate programs by presenting a model for evaluating the conditions under which a firm should offer rebates in a competitive environment. Specifically, we consider a two‐level supply chain comprising one manufacturer and one retailer. Each firm makes three decisions: the regular (wholesale or retail) price, whether or not to offer rebates, and the rebate value should the firm decide to launch a rebate program. We determine the equilibrium of a vertical competition game between the manufacturer (leader) and the retailer (follower), and we provide insights about how competition affects the conditions under which a firm should offer rebates in equilibrium.     

Supply chain coordination through cooperative advertising with reference price effect

Cooperative advertising, which usually occurs in a vertical supply chain, is typically a cost sharing and promotion mechanism for the manufacturer to affect retail performance. Research in the literature, however, rarely considers the important phenomenon that advertising has a positive effect on the consumer's reference price. In fact, when a consumer makes a decision to buy a product or not, a reference price is usually in his mind and plays a determinant role. Taking into account the impact of advertising on the reference price, this paper proposes a dynamic cooperative advertising model for a manufacturer–retailer supply chain and analyzes how the reference price effect would influence the decisions of all the channel members. In our model, both the consumer's goodwill and reference price for the product are assumed to be influenced by the advertising and are modeled in differential dynamic equations. In addition, the advertising level, the consumer's goodwill and the reference price are all assumed to have positive effect on sales. Utilizing differential game theory, this paper formulates the optimal decisions of the manufacturer and the retailer in two different game scenarios: Stackelberg game and cooperative game. Also, this paper proposes a new mechanism to coordinate the supply chain in which both the manufacturer and the retailer share each other's advertising costs.     

The Role of Slotting Fees in the Coordination of Assortment Decisions

Large numbers of new products introduced annually by manufacturers may strain the relationship between retailers and manufacturers regarding assortments carried by retailers. For example, many retailers in the grocery industry will agree to broaden their assortments only if the manufacturer agrees to pay slotting fees for the new products. We investigate the role played by slotting fees in coordinating the assortment decisions in a supply chain. To do so, we study a single‐retailer, single‐manufacturer supply chain, where the retailer decides what assortment to offer to end customers. Double marginalization results in a discrepancy between the retailer's optimal assortment and the assortment that maximizes total supply chain profits. We consider a payment scheme that is analogous to slotting fees used in the grocery industry: the manufacturer pays the retailer a per‐product fee for every product offered by the retailer in excess of a certain target level. We show that, if the wholesale price is below some threshold level, this payment scheme induces the retailer to offer the supply‐chain‐optimal assortment and makes both parties better off.     

考虑异质消费者的线下到线上供应链合作广告契约设计

本文针对一个拥有线上渠道的制造商和一个零售商组成的线下到线上(O2O)供应链,考虑渠道产品差异化策略下零售商为制造商线上渠道进行广告引流,刻画消费者对产品的异质性需求,分别设计对称信息和不对称信息下制造商的最优合作广告契约,通过对比两种情形中最优决策及利润的变化分析信息不对称的影响,并进一步探讨不对称信息下消费者渠道转换的麻烦成本、单位不匹配成本等重要参数对合作广告契约设计和供应链成员利润的影响。研究发现:不对称信息下,制造商可以策略性选择三种不同策略以最大化自身利润,其中不甄别零售商真实信息的混同均衡在某些条件下是制造商的最优策略;尽管信息不对称会给制造商带来利润损失,但制造商通过策略选择可缓和信息不对称的不利影响,某些条件下信息不对称并不损害供应链总体的利润;麻烦成本的变化会改变制造商不对称信息下最优合作广告契约的策略选择,某些条件下麻烦成本的增高对制造商利润反而存在正影响。最后,通过数值仿真对上述研究结果进行直观考察和说明。