Game-theoretic analysis of cooperation among supply chain agents: Review and extensions

This paper surveys some applications of cooperative game theory to supply chain management. Special emphasis is placed on two important aspects of cooperative games: profit allocation and stability. The paper first describes the construction of the set of feasible outcomes in commonly seen supply chain models, and then uses cooperative bargaining models to find allocations of the profit pie between supply chain partners. In doing so, several models are analyzed and surveyed, and include suppliers selling to competing retailers, and assemblers negotiating with component manufacturers selling complementary components. The second part of the paper discusses the issue of coalition formation among supply chain partners. An exhaustive survey of commonly used stability concepts is presented. Further, new ideas such as farsightedness among supply chain players are also discussed and analyzed. The paper also opens some avenues of future research in applying cooperative game theory to supply chain management.     

A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer-retailer supply chains

Vertical cooperative (co-op) advertising is a marketing strategy in which the retailer runs local advertising and the manufacturer pays for a portion of its entire costs. This paper considers vertical co-op advertising along with pricing decisions in a supply chain; this consists of one manufacturer and one retailer where demand is influenced by both price and advertisement. Four game-theoretic models are established in order to study the effect of supply chain power balance on the optimal decisions of supply chain members. Comparisons and insights are developed. These embrace three non-cooperative games including Nash, Stackelberg-manufacturer and Stackelberg-retailer, and one cooperative game. In the latter case, both the manufacturer and the retailer reach the highest profit level; subsequently, the feasibility of bargaining game is discussed in a bid to determine a scheme to share the extra joint profit.     

考虑延迟现象的质量改进投入和营销努力动态协同策略

利用时滞微分方程刻画质量改进投入对品牌商誉提升的延迟现象,分别构建了制造商和零售商采取非合作博弈、合作博弈以及成本分担的部分合作博弈(制造商参与营销的单向部分合作博弈、零售商参与生产的单向部分合作博弈、制造商参与营销及零售商参与生产的双向部分合作博弈)五种决策模式下的微分博弈模型。借助哈密尔顿极大值原理,求解得到五种情形下的制造商最优质量改进投入策略和零售商的最优营销努力策略以及供应链利润。对比五种博弈模式下的结果发现:1)延时现象会降低制造商进行质量改进投入的积极性,但对零售商营销努力无影响;品牌商誉在延迟现象影响下出现先衰减后提升的演进规律;2)合作博弈对于供应链绩效总是最优的,三种成本分担的部分合作博弈契约虽不能实现供应链的完全协调,但可以对非合作博弈情形进行帕累托改进;3)对比两种单向部分合作博弈,在提高供应链利润方面,制造商参与营销的成本分担契约优于零售商参与生产的成本分担契约;4)三种成本分担契约中,双向合作的部分合作博弈是供应链的最优选择,但随着延迟时间增大,其帕累托改进效果将不再明显。     

具有限制结盟结构的供应链合作创新及其收益分配

针对具有限制结盟结构特征的三级供应链合作创新联盟问题,分析了由单个供应商、制造商和销售商组成的不同联盟系统下的收益情况,并运用图合作博弈的average tree solution(简称“A-T解”)法对各成员的收益进行了分配。结果表明,所有成员参与供应链联盟时总收益最大,且A-T解分配法与Shapley值法相比更具合理性和有效性,能充分突出成员在合作联盟中的特殊地位(位置)及其重要性,该结论进一步通过比较不同级别结构下的供应链收益分配问题进行说明。     

具有限制结盟结构的供应链合作创新及其收益分配

针对具有限制结盟结构特征的三级供应链合作创新联盟问题,分析了由单个供应商、制造商和销售商组成的不同联盟系统下的收益情况,并运用图合作博弈的average tree solution(简称“A-T解”)法对各成员的收益进行了分配。结果表明,所有成员参与供应链联盟时总收益最大,且A-T解分配法与Shapley值法相比更具合理性和有效性,能充分突出成员在合作联盟中的特殊地位(位置)及其重要性,该结论进一步通过比较不同级别结构下的供应链收益分配问题进行说明。     

Optimal contracts and the manufacturer’s pricing strategies in a supply chain with an inequity-averse retailer

Studies in the supply chain literature have typically focused on profit or revenue maximization and assumed that agents within the supply chain are self-interested and only care about their own monetary payoffs. Research in these areas, however, rarely considers an important phenomenon called inequity aversion in which the object pursued by agents within the supply chain is not only their own profit maximization but also the equity of profit allocation. In fact, when agents within a supply chain collaborate with each other to serve a market, the scheme of profit allocation between them usually plays a determinate role in cooperation. Taking into account the impact of agents’ behavior of inequity aversion on the coordination of the supply chain, this paper investigates the optimal contracts and the manufacturer’s pricing strategies in a single-manufacturer and single-retailer supply chain. In this way, we obtain two interesting results: (1) the retailer’s equity aversion largely affects the manufacturer’s decision making, which is not always bad for the manufacturer; and (2) the retailer’s inequity aversion as well as the consumer’s price-sensitive coefficient plays a dominant role in the manufacturer’s decision making.     

风险中性零售商的合作广告策略与订货模型

考虑了由一个制造商与一个零售商构成的单期二阶段供应链是否进行合作广告的博弈问题.面对市场需求的不确定性,零售商从制造商处订购报童类型产品销售给消费者,零售商具有风险中性的行为特征.通过不合作广告与合作广告两种情形,制造商与零售商进Stackelberg主从博弈,得到了均衡解,比较后发现,合作广告下的最优解及利润总是优于不合作广告下的最优解和利润,告诉了上下游企业采用合作广告的广告策略.最后,通过数值算例,给出了需求敏感系数对最优决策的影响,同时也论证了有关结论.     

Research on coordination mechanism in three-level green supply chain under non-cooperative game

In view of the three-level green supply chain system in which market demand correlates with product green degree, game theory is applied to study four models, namely cooperative decision-making, three-level leader–follower game, Stackelberg game I and Stackelberg game II. Theoretical analysis shows that the profits of both the supply chain system and participating members reach the optimal level under cooperative decision-making, while the decision results of participating members as well as the channel profit are far from satisfactory under the non-cooperative game. By building a revenue sharing mechanism, Shapley value method coordination mechanism and asymmetric Nash negotiation mechanism, supply chain members are motivated to respond positively to the cooperation in producing and marketing green products, the optimal income distribution coefficient of participating members is given, and the income of each member is increased substantially as is compared with that under the non-cooperative game. Also, by determining the cooperative parameter, green supply chain managers may effectively get involved in the aforementioned coordination mechanisms to intervene and regulate the green channel so as to promote the smooth operation of green supply chain.     

由零售商负责回收的多期闭环供应链网络均衡

本文研究了零售商回收模式下多期闭环供应链网络均衡问题。制造商通过零售渠道将产品销售给消费者,以满足消费市场需求,同时消费产生的废旧品由零售商回收返回制造商处进行再制造,通过产品库存和回收废旧品连接相邻规划期。运用变分不等式理论和互补理论,分别刻画了制造市场、零售市场和消费市场的均衡,接着构建了多期闭环供应链网络均衡模型。利用变分不等式的投影收缩算法,对模型进行求解。算例着重分析了废旧品利用率对网络均衡状态和供应链成员利润的影响。结果表明:当制造商的废旧品利用率逐渐增加时,回收量逐渐增加,制造商的利润先减后增,零售商利润一直增加,而供应链总利润一直增加,供应链网络中的最优决策变量主要受到回收量约束的影响。     

考虑互惠偏好的闭环供应链系统合作机制研究

将互惠偏好引入到闭环供应链系统合作机制中,研究了由一个制造商,一个零售商和一个再制造商组成的三层闭环供应链,运用Stackelberg博弈理论分析了闭环供应链整体及各成员的最优决策问题,并对5种情形(决策模式)下的均衡结果进行比较分析.研究发现在考虑互惠偏好行为下,分散决策模式和局部联盟决策模式下的系统利润低于集中决策模式下的收益;新产品和再制造产品的销售量(零售价格)与制造商对零售商的互惠偏好系数呈正(负)相关,与零售商对制造商的互惠偏好系数呈负(正)相关;5种决策模式的供应链系统利润与制造商对零售商的互惠偏好系数呈正相关,与零售商对制造商的互惠偏好系数呈负相关.     

三级供应链合作利润博弈与分配机制构建

基于变形需求函数建立了多向主从式三级供应链下游成员合作利润博弈模型,运用Stackelberg博弈法求解,对成员及渠道利润随合作关系程度变化进行深入的经济分析;构建了具有理性、转移性、协商性的供应链下游合作利润分配机制定量模型,其由合作利润结构性分配和合作利润运行性分配组成,阐明了之间的互动关系与内在运行方式,得出当合作关系程度高于2/3时才进行合作利润运行性分配的结论,且对分配机制的内在运行方式进行了数学解析。     

基于微分博弈的二级猪肉供应链质量行为协调机制研究

运用微分博弈方法研究了由单一生猪屠宰加工企业和单一超市构成的二级猪肉供应链质量行为协调机制。首先考察并比较了Nash非合作博弈、Stackelberg主从博弈以及协同合作博弈情形下屠宰加工企业和超市的最优质量行为决策,研究结果表明协同合作决策模式下,屠宰加工企业和超市的质量行为以及猪肉供应链总体利润均严格优于在非合作决策模式下的相应值。然后导出了能够使屠宰加工企业和超市的个体利润达到帕累托最优,进而实现双方质量行为协调的供应链总体利润分配系数的取值范围。     

Coordination of cooperative advertising in a two-level supply chain when manufacturer offers discount

We studied the coordination of cooperative advertisement in a manufacturer–retailer supply chain when the manufacturer offers price deductions to customers. With a price sensitive market, the expected demand with cooperative advertising and price deduction is demonstrated. When the manufacturer is a leader, we obtained the optimal national brand name investment, local advertisement and associated manufacturer’s allowance with any given price deduction. When the manufacturer offers more price deduction to customers, the retailer will increase local advertisement if the manufacturer provides the same portion of the local advertising allowance. We obtained the necessary and sufficient condition for the price deduction to ensure an increase of manufacturer’s profit, and a search procedure for determining such an optimal price deduction is provided as well. When the manufacturer and retailer are partners, we obtained the optimal national brand name investment and local advertisement. For any given price deduction, the total profit for the supply chain with cooperative scheme is always higher than that with the non-cooperative scheme. When price elasticity of demand is larger than one, the resulting closed form optimal price deduction with partnership is also obtained. To increase profits for both parties in a supply chain, we recommend that coordination in local and national cooperative advertising with a partnership relationship between manufacturer and retailer is the best solution. The bargaining results show how to share the profit gain between the manufacturer and the retailer, and determine the associated pricing and advertising policies for both parties.     

Optimal business policies for a supplier–transporter–buyer channel with a price-sensitive demand

As the third party logistics partners (carriers) taking a more and more significant role in supply chain practices and customer service performance improvement, there is an emerging need for the studies on optimal channel coordination policies for business processes involving not only supplier and buyer (retailer), but also transportation partners. In this paper, we explicitly add a transportation partner with concave cost functions into the analysis for supplier–buyer channel coordination policies, and analyse the impact of coordination and pricing policies on supply chain profitability. The market demand is assumed to be a decreasing convex function of buyer's selling price (x), D(x)=d/x². Under this assumption, we quantify the improvement on total supply chain profitability when moving from a non-cooperative environment to a fully cooperative environment, and show that the joint annual profit of three partners in a cooperative environment can be at least twice of what may be achieved by three independently operated companies in a leader–follower business game. While in a real-world business environment, a perfect collaboration is hard to achieve, this result can be used to provide a quick estimation on the upper bound on the budget for profit sharing or discount offers among the supply chain partners.     

Equilibrium analysis and corporate social responsibility for supply chain integration

This paper evaluates the profit of coordination between manufacturers on corporate social responsibility (CSR) under network equilibrium. A three-tier supply chain network with multiple manufacturers, distributors, and retailers is considered, and several mathematical models are established to investigate behavior and profits in a decentralized supply chain network, a centralized supply chain network, and a supply chain network with CSR. The system-optimal solution of a supply chain network problem is usually not achievable or stable since each member always tries to maximize its own profit. In order to make such a system-optimal solution in a stable state and ensure the maximization of total profits, a strategy of coordination between manufacturers on CSR is proposed. The amount of payment in CSR of each manufacturer is clearly defined. A hybrid diagonalization method with a super-network representation is proposed and tested with numerical examples. The results show that by taking CSR, the total profits of the whole supply chain network can increase with or without coordination.     

Vertical cooperative advertising and pricing decisions in a manufacturer–retailer supply chain: A game-theoretic approach

Manufacturers can increase the advertising expenditures of their retailers by bearing a fraction of the occurring costs within the framework of a vertical cooperative advertising program. We expand the existing research which deals with advertising and pricing decisions in a manufacturer–retailer supply chain contemporaneously. By means of game theory, four different relationships between the channel members are considered: Firstly, three non-cooperative games with either symmetrical distribution of power or asymmetrical distribution with one player being the leader in each case, and one cooperative game where both players tend to maximize the total profit. The latter is complemented by a bargaining model, which proposes a fair split of profit on the basis of the players’ risk attitude and bargaining power. Our main findings are as follows: (a) In contrast to previous analyses, we do not limit the ratio between manufacturer’s and retailer’s margin, which provides more general insights into the effects of the underlying distribution of power within the channel. (b) The highest total profit is gained when both players cooperate. This behavior puts also the customers in a better position, as it produces the lowest retail price as well as the highest advertising expenditures compared to the other configurations.     

含有混合销售渠道的供应链合作策略研究

本文通过Stackelberg博弈方法研究含有混合销售渠道的供应链中双渠道制造商参与的不同合作策略对供应链中企业的定价和利润的影响。研究表明:在有双渠道制造商参与的合作中,合作策略不仅增加了合作联盟的利润,而且也能够增加合作联盟外其他成员的利润;供应链中参与合作的企业越多,给供应链带来的总利润也越大;在参与合作联盟的成员数相同的条件下,供应链的纵向合作比横向合作给供应链能够带来更多的利润。最后,通过数值实验验证了上述结论。     

不同情形下供应链优化决策模型的比较分析

本文提出三种不同情形（制造商与零售商追求各自利润最大化，并且没有价格折扣策略；制造商与零售商共同追求总利润最大化，不实施价格折扣策略；制造商与零售商共同追求总利润最大化，并实施价格折扣策略）下供应链价格和库存补充策略的优化决策模型，并通过具体数例进行比较分析，结果表明，供应链合作并实施价格折扣策略时的供应链总利润最高，而供应链双方利润分配系数的变化对基于供应链总利润最大化的供应链优化决策没有影响．     

产学研合作收益分配的博弈分析

产学研的合作促进了科研成果的产业化进程,同时也加速了企业的产品创新.但由于收益分配的不合理,导致了许多产学研合作的失败.从博弈论的观点来看产学研的组建和运行过程,建立了合作收益最优分配系数模型,分析了考虑学研方技术风险条件下的合作收益分配系数,并对合作各方在协议的收益分配方案下会如何进行自己的最优行动选择进行了非合作博弈分析.     

Non-cooperative matching games

Consider a market in which two distinct groups of agents face each other. Every agent can improve upon his status quo if he is matched with a member of the opposite group and if he agrees with his partner how to split the realized gain. The paper presents two non-cooperative games in which the agents construct the allocation without the help of an auctioneer. In the first game the set of equilibria coincides with the cooperative “stable solutions” which are well-established in this context. In the second game it is shown that a change of the order of the moves is sufficient to arrive at a unique equilibrium payoff.