供应链投资的微分博弈模型研究
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摘要
一条完整的供应链由多个节点组成,不同节点的企业间形成供应链的纵向关系,同一节点内的企业间形成供应链横向关系。加强纵向合作、削弱横向竞争是供应链取得成功的关键。由于供应链各成员是独立自主的企业,其目标都是最大化自身利润,这往往偏离甚至违背供应链的整体利益。因此,需要协调手段来保证供应链能成功优化。本文考虑广告与研发两种类型的投资,通过建立相关的微分博弈模型来研究供应链动态的投资合作及其相应的供应链协调手段,主要创新点如下：
研究由一个供应商和一个面临随机指数需求的零售商组成的供应链系统的契约协调问题。供应链契约用来消除因节点间存在交易成本而导致的非效率“双边际效应”,结果表明,在收益共享或者成本分摊契约下,供应链独立决策时的效率可以无限接近100%,但供应链效率的提高以牺牲博弈弱势方的利润为代价；核心企业可以通过强迫签订不平等契约的非协调方式提高供应链效率,也可以通过对供应链的利润增量再分配的协调方式达到100%的供应链效率。
讨论了产品具有替代效应的两个生产商进行双寡头广告战的问题。广告战中,竞争广告用来削弱对手的品牌声誉,信息广告用来加强自身的品牌声誉。在生产商具有对称性的条件下,分析了广告效率、广告的自然衰减速度、贴现率等参数对广告战的稳态策略的影响；在生产商不具对称性的条件下,占据效率、成本或者替代优势的生产商执行进攻策略,劣势生产商则执行防守策略,并进一步分析了优势扩大时如何在进攻与防守策略之间取得平衡。
建立了一个生产商与一个零售商进行产品广告合作的微分博弈模型,产品的品牌声誉决定市场容量,需求由市场容量与广告努力共同决定。研究表明：i)与虚拟一体化决策相比,独立决策时供应链广告投资存在“搭便车”现象,从而降低了供应链的效率。ii)有两种类型的“搭便车”,一种是供应链中存在效率或者成本优势明显的企业,“搭便车”仅限于劣势企业；另一种则是供应链中不存在优势明显的企业,表现为互搭对方的便车。iii)对于第一种“搭便车”现象,由于提高供应链的效率会牺牲劣势企业的利益,核心(优势)企业可以通过补贴劣势企业损失的方式来做供应链协调；对于第二种“搭便车”现象,由于提高供应链的效率会同时增加两企业的利润,因此可以通过设置双向激励策略,使供应链自动达到100%的效率。
在生产商做广告并考虑零售商销售的产品具有扩散效应的基础上,建立了一个生产商与N个零售商的合作博弈模型。在这个基础的微分博弈模型中,品牌声誉由生产商的广告努力和零售商的销售量共同决定,产品的价格由品牌声誉和销量通过逆需求函数决定。对基础模型进行了如下研究：i)首次从供应链信息不对称角度研究微分博弈,指明除严格意义的开环、闭环均衡外,还存在众多的其它均衡,丰富了可供分析对象。ii)挑选出基础模型三个有趣的均衡,即保守均衡、开环均衡与闭环均衡,并就信息的价值对这三个均衡进行讨论,得到核心企业判断最优均衡的方法,以及选择这个均衡该采取怎样的协调手段。iii)讨论了信息不对称条件下零售商的结盟行为,不同的扩散效应下,零售商结盟加剧或者舒缓了供应链横向竞争。iv)讨论了基础模型中销量或者价格固定时供应链一体化的两个特例,指明将前述三个均衡中任意一个的销量固定后进行一体化决策,都能对该均衡进行Pareto改进；并就道德风险与监管成本分别对这两个特例的一体化稳态策略进行可行性分析。其次,将基础模型中产品的扩散效应去掉,考虑零售商做促销广告。促销广告有两种效果,第一种效果与生产商的广告效果相同,影响产品的品牌声誉；第二种效果与生产商相异,使产品差异化。研究表明,若促销影响品牌声誉,生产商有明显的“搭便车”现象；若促销导致差异化,只有特定条件下才存在生产商“搭便车”现象。
构造了一个由N个供应商与一个生产商合作研发的非线性微分博弈模型。研发降低产品零部件的生产成本,供应链有两种研发模式,即生产商单独研发模式与生产商、供应商共同研发模式。研究得到以下结果：i)确定了两种研发模式下,供应链博弈存在鞍点的条件,从而判别生产商与供应商的合作博弈是否存在稳定的均衡。具体而言,共同研发比单独研发更容易获得稳定的均衡。ii)就模型各参数对鞍点处生产商与供应商的研发努力以及生产成本的稳态表达式进行了比较静态分析,并对在Arrow与Schumpeter关于垄断是否有利于技术进步的著名论战中的站队进行讨论。iii)定性分析了研发模式的选择问题,并就此问题的供应链协调给出了指导性建议。
A complete chain of supply consists of many nodes. Enterprises from different nodes form a vertical relation while those from the same nodes form a horizontal relation of supply chain. To enhance vertical cooperation and weaken horizontal competition is a key point of a supply chain to succeed. Since members of a supply chain are independent enterprises who all aim at maximizing their benefit, this often deviates and even violates the group benefit of the supply chain. Therefore coordination measures are needed to ensure the supply chain to optimize successfully. In this thesis, we consider two types of investment:advertisement and research and development (R&D for short). By constructing related differential gaming model, we study dynamic investment cooperation of the supply chain and the corresponding channel coordination measures. The main Innovations of this thesis are as follows:
We studies the contract coordination problem of the supply chain system composed of a suppler and a retailer with a random exponential demand. The supply chain contract is used to eliminate the ineffective bilateral effect caused by transaction cost at the nodes. The result shows that under the contract of sharing the benefit and cost, the efficiency of independent channel decision can infinitely approach one hundred percent. But the improvement of channel efficiency has to sacrifice the benefit of the weaker side of gaming as the cost. The core enterprises may improve the channel efficiency by means of non-coordination such as coercing to sign unfair contracts, or by coordination to reallocate the profit increment of channels so as to attain one hundred percent channel efficiency.
We discusses the problem of advertisement battle of duopoly between two manufacturers with product replacement effect. In the ads battle, competition ads are used to weaken the brands reputation of the rival, and information ads are used to strengthen his own brands reputation. For manufacturers with symmetry, we analyze the influence of ads parameters like efficiency, natural decay rate and discount on the stability policy of ads battle; for manufacturers without symmetry, as those occupying the advantage of efficiency and cost will take the attack policy while those with disadvantage on the above aspects will take the defense policy, we analyze further how to keep the balance between the attacker and the defender when the advantage increases.
A differential gaming model on the product ads cooperation between the manufacturer and the retailer is constructed, where the brands reputation of product determines the capacity of market and the demands are determined by the capacity of market and the effect of ads. The study shows that:(ⅰ) Compared with the decision of virtual integration, there exists the phenomenon of rider in the ads investment in independent decision, resulting in the decrease of channel efficiency,(ⅱ) There are two types of riders. One type is that there exists an enterprise with obvious advantage on efficiency and cost, so the disadvantageous enterprise is the only rider; the other type is that there is no enterprise with obvious advantage, so they are mutual riders,(ⅲ) For the first type of rider, since the improvement of channel efficiency will sacrifice the benefit of the disadvantageous enterprise, the core (advantageous) enterprise can make the channel coordination by compensating the disadvantageous enterprise; for the second type of rider, since the improvement of channel efficiency will increase the profit of both sides at the same time, bilateral excitation policy can be set to make channels to attain one hundred percent efficiency.
On the basis of the manufacturer advertising and products of retailers having diffusion effect, we construct a cooperative gaming model between a manufacture and N retailers. In this basic differential gaming model, brands reputation is determined by the advertisement of the manufacture and the sales of retailers, and the price of the product is determined by the brands reputation and sales via the inverse demand function. The basi model is studied as follows:(ⅰ) We initiate the study of differential gaming from the angle of asymmetric information in the supply chain, and point out that there are many other balances besides the open ring, closed ring equilibrium in the strict sense, thus expanding the objects available for analysis,(ⅱ) Three interesting equilibriums are selected from the basic model, i.e. conservative, open and closed equilibrium of which discussions are made on the value of information. The method of determining the best equilibrium and the measures to be taken for this chosen equilibrium is obtained for the core enterprise,(ⅲ) We discuss the alliance behavior of retailers with the asymmetric information. On different diffusion effects, the alliance behavior of retailers may aggravate or alleviate the horizontal competition of supply chain,(ⅳ) Two special examples of channels integration in the basic model when sales or price is fixed are discussed, showing that if the sales is fixed in any of the above-mentioned equilibrium, the integration policy can improve the equilibrium in the sense of Pareto. The feasibility of the stability policy of integration in these two special examples is analyzed on the moral hazard and regulatory cost. Next, remove the diffusion effect of products in the basic model and consider the promotion advertisement of retailers. The promotion ads have two effects. The first one is the same as that of ads of manufacturer, affecting the brands reputation of products; the second one is different, making the products diverse. Our research shows that if the promotion affects brands reputation, the manufacturer is the rider obviously, and if the promotion leads to diversity, then the manufacturer can only be the rider in particular cases.
A nonlinear differential gaming model on the cooperative research and development (R&D) between a manufacturer and N retailers is constructed. The R&D of reducing the cost of parts of products, channels have two models of R&D, i.e. the manufacturer alone and the cooperation between the manufacturer and supplier. We have the following results:(ⅰ) Determining the conditions on the existence of saddle points of channel gaming in two R&D models, hence determining whether there exists a stable equilibrium in the cooperative gaming between the manufacturer and the suppler. Concretely, cooperative R&D acquires stable equilibrium more easily than independent R&D.(ⅱ) For various parameters in the model, comparing and making a static analysis on the R&D of the manufacturer and the suppler, and the stability expression of production cost at the saddle points. A discussion is made on the sides of Arrow and Schumpeter take in the famous debate on whether monopoly is beneficial to the progress of technology,(ⅲ) Analyzing qualitatively on the problem of mode choice in R&D. Instructive suggestions on the channel coordination of this problem are given.
研究由一个供应商和一个面临随机指数需求的零售商组成的供应链系统的契约协调问题。供应链契约用来消除因节点间存在交易成本而导致的非效率“双边际效应”,结果表明,在收益共享或者成本分摊契约下,供应链独立决策时的效率可以无限接近100%,但供应链效率的提高以牺牲博弈弱势方的利润为代价；核心企业可以通过强迫签订不平等契约的非协调方式提高供应链效率,也可以通过对供应链的利润增量再分配的协调方式达到100%的供应链效率。
讨论了产品具有替代效应的两个生产商进行双寡头广告战的问题。广告战中,竞争广告用来削弱对手的品牌声誉,信息广告用来加强自身的品牌声誉。在生产商具有对称性的条件下,分析了广告效率、广告的自然衰减速度、贴现率等参数对广告战的稳态策略的影响；在生产商不具对称性的条件下,占据效率、成本或者替代优势的生产商执行进攻策略,劣势生产商则执行防守策略,并进一步分析了优势扩大时如何在进攻与防守策略之间取得平衡。
建立了一个生产商与一个零售商进行产品广告合作的微分博弈模型,产品的品牌声誉决定市场容量,需求由市场容量与广告努力共同决定。研究表明：i)与虚拟一体化决策相比,独立决策时供应链广告投资存在“搭便车”现象,从而降低了供应链的效率。ii)有两种类型的“搭便车”,一种是供应链中存在效率或者成本优势明显的企业,“搭便车”仅限于劣势企业；另一种则是供应链中不存在优势明显的企业,表现为互搭对方的便车。iii)对于第一种“搭便车”现象,由于提高供应链的效率会牺牲劣势企业的利益,核心(优势)企业可以通过补贴劣势企业损失的方式来做供应链协调；对于第二种“搭便车”现象,由于提高供应链的效率会同时增加两企业的利润,因此可以通过设置双向激励策略,使供应链自动达到100%的效率。
在生产商做广告并考虑零售商销售的产品具有扩散效应的基础上,建立了一个生产商与N个零售商的合作博弈模型。在这个基础的微分博弈模型中,品牌声誉由生产商的广告努力和零售商的销售量共同决定,产品的价格由品牌声誉和销量通过逆需求函数决定。对基础模型进行了如下研究：i)首次从供应链信息不对称角度研究微分博弈,指明除严格意义的开环、闭环均衡外,还存在众多的其它均衡,丰富了可供分析对象。ii)挑选出基础模型三个有趣的均衡,即保守均衡、开环均衡与闭环均衡,并就信息的价值对这三个均衡进行讨论,得到核心企业判断最优均衡的方法,以及选择这个均衡该采取怎样的协调手段。iii)讨论了信息不对称条件下零售商的结盟行为,不同的扩散效应下,零售商结盟加剧或者舒缓了供应链横向竞争。iv)讨论了基础模型中销量或者价格固定时供应链一体化的两个特例,指明将前述三个均衡中任意一个的销量固定后进行一体化决策,都能对该均衡进行Pareto改进；并就道德风险与监管成本分别对这两个特例的一体化稳态策略进行可行性分析。其次,将基础模型中产品的扩散效应去掉,考虑零售商做促销广告。促销广告有两种效果,第一种效果与生产商的广告效果相同,影响产品的品牌声誉；第二种效果与生产商相异,使产品差异化。研究表明,若促销影响品牌声誉,生产商有明显的“搭便车”现象；若促销导致差异化,只有特定条件下才存在生产商“搭便车”现象。
构造了一个由N个供应商与一个生产商合作研发的非线性微分博弈模型。研发降低产品零部件的生产成本,供应链有两种研发模式,即生产商单独研发模式与生产商、供应商共同研发模式。研究得到以下结果：i)确定了两种研发模式下,供应链博弈存在鞍点的条件,从而判别生产商与供应商的合作博弈是否存在稳定的均衡。具体而言,共同研发比单独研发更容易获得稳定的均衡。ii)就模型各参数对鞍点处生产商与供应商的研发努力以及生产成本的稳态表达式进行了比较静态分析,并对在Arrow与Schumpeter关于垄断是否有利于技术进步的著名论战中的站队进行讨论。iii)定性分析了研发模式的选择问题,并就此问题的供应链协调给出了指导性建议。
A complete chain of supply consists of many nodes. Enterprises from different nodes form a vertical relation while those from the same nodes form a horizontal relation of supply chain. To enhance vertical cooperation and weaken horizontal competition is a key point of a supply chain to succeed. Since members of a supply chain are independent enterprises who all aim at maximizing their benefit, this often deviates and even violates the group benefit of the supply chain. Therefore coordination measures are needed to ensure the supply chain to optimize successfully. In this thesis, we consider two types of investment:advertisement and research and development (R&D for short). By constructing related differential gaming model, we study dynamic investment cooperation of the supply chain and the corresponding channel coordination measures. The main Innovations of this thesis are as follows:
We studies the contract coordination problem of the supply chain system composed of a suppler and a retailer with a random exponential demand. The supply chain contract is used to eliminate the ineffective bilateral effect caused by transaction cost at the nodes. The result shows that under the contract of sharing the benefit and cost, the efficiency of independent channel decision can infinitely approach one hundred percent. But the improvement of channel efficiency has to sacrifice the benefit of the weaker side of gaming as the cost. The core enterprises may improve the channel efficiency by means of non-coordination such as coercing to sign unfair contracts, or by coordination to reallocate the profit increment of channels so as to attain one hundred percent channel efficiency.
We discusses the problem of advertisement battle of duopoly between two manufacturers with product replacement effect. In the ads battle, competition ads are used to weaken the brands reputation of the rival, and information ads are used to strengthen his own brands reputation. For manufacturers with symmetry, we analyze the influence of ads parameters like efficiency, natural decay rate and discount on the stability policy of ads battle; for manufacturers without symmetry, as those occupying the advantage of efficiency and cost will take the attack policy while those with disadvantage on the above aspects will take the defense policy, we analyze further how to keep the balance between the attacker and the defender when the advantage increases.
A differential gaming model on the product ads cooperation between the manufacturer and the retailer is constructed, where the brands reputation of product determines the capacity of market and the demands are determined by the capacity of market and the effect of ads. The study shows that:(ⅰ) Compared with the decision of virtual integration, there exists the phenomenon of rider in the ads investment in independent decision, resulting in the decrease of channel efficiency,(ⅱ) There are two types of riders. One type is that there exists an enterprise with obvious advantage on efficiency and cost, so the disadvantageous enterprise is the only rider; the other type is that there is no enterprise with obvious advantage, so they are mutual riders,(ⅲ) For the first type of rider, since the improvement of channel efficiency will sacrifice the benefit of the disadvantageous enterprise, the core (advantageous) enterprise can make the channel coordination by compensating the disadvantageous enterprise; for the second type of rider, since the improvement of channel efficiency will increase the profit of both sides at the same time, bilateral excitation policy can be set to make channels to attain one hundred percent efficiency.
On the basis of the manufacturer advertising and products of retailers having diffusion effect, we construct a cooperative gaming model between a manufacture and N retailers. In this basic differential gaming model, brands reputation is determined by the advertisement of the manufacture and the sales of retailers, and the price of the product is determined by the brands reputation and sales via the inverse demand function. The basi model is studied as follows:(ⅰ) We initiate the study of differential gaming from the angle of asymmetric information in the supply chain, and point out that there are many other balances besides the open ring, closed ring equilibrium in the strict sense, thus expanding the objects available for analysis,(ⅱ) Three interesting equilibriums are selected from the basic model, i.e. conservative, open and closed equilibrium of which discussions are made on the value of information. The method of determining the best equilibrium and the measures to be taken for this chosen equilibrium is obtained for the core enterprise,(ⅲ) We discuss the alliance behavior of retailers with the asymmetric information. On different diffusion effects, the alliance behavior of retailers may aggravate or alleviate the horizontal competition of supply chain,(ⅳ) Two special examples of channels integration in the basic model when sales or price is fixed are discussed, showing that if the sales is fixed in any of the above-mentioned equilibrium, the integration policy can improve the equilibrium in the sense of Pareto. The feasibility of the stability policy of integration in these two special examples is analyzed on the moral hazard and regulatory cost. Next, remove the diffusion effect of products in the basic model and consider the promotion advertisement of retailers. The promotion ads have two effects. The first one is the same as that of ads of manufacturer, affecting the brands reputation of products; the second one is different, making the products diverse. Our research shows that if the promotion affects brands reputation, the manufacturer is the rider obviously, and if the promotion leads to diversity, then the manufacturer can only be the rider in particular cases.
A nonlinear differential gaming model on the cooperative research and development (R&D) between a manufacturer and N retailers is constructed. The R&D of reducing the cost of parts of products, channels have two models of R&D, i.e. the manufacturer alone and the cooperation between the manufacturer and supplier. We have the following results:(ⅰ) Determining the conditions on the existence of saddle points of channel gaming in two R&D models, hence determining whether there exists a stable equilibrium in the cooperative gaming between the manufacturer and the suppler. Concretely, cooperative R&D acquires stable equilibrium more easily than independent R&D.(ⅱ) For various parameters in the model, comparing and making a static analysis on the R&D of the manufacturer and the suppler, and the stability expression of production cost at the saddle points. A discussion is made on the sides of Arrow and Schumpeter take in the famous debate on whether monopoly is beneficial to the progress of technology,(ⅲ) Analyzing qualitatively on the problem of mode choice in R&D. Instructive suggestions on the channel coordination of this problem are given.
引文
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