慧学（33）：精读博士论文直播背景下的平台销售模式选择（2）

摘要：In this issue, the editor will introduce the platform sales model selection considering consumer return behavior in the context of

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“慧学（33）：精读博士论文《考虑消费者行为的平台供应链销售策略优化研究》直播背景下考虑消费者退货行为的平台销售模式选择（2）”

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” Hui Xue (33): Intensive reading of doctoral dissertation

‘Optimization of Platform Supply Chain Sales Strategies Based on Consumer behavior’ platform sales model selection considering consumer return behavior in the context of live streaming （2）”

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本期推文小编将从思维导图、精读内容、知识补充三个方面为大家介绍博士论文《考虑消费者行为的平台供应链销售策略优化研究》直播背景下考虑消费者退货行为的平台销售模式选择（2）。

In this issue, the editor will introduce the platform sales model selection considering consumer return behavior in the context of live streaming (2) of the doctoral dissertation "Optimization of Platform Supply Chain Sales Strategies Based on Consumer behavior" from three aspects: mind mapping, intensive reading content, and knowledge supplement.

一、思维导图（Mind mapping）

二、精读内容（Intensive reading content）

1、消费者退货对定价策略选择的影响（The impact of consumer returns on pricing strategy selection）

引理3.3说明，在模式R中，三种定价策略的直播努力水平存在固定的高低顺序：策略D高于策略SH，而策略SH又高于策略SL。相比之下，在模式A中，最优努力水平受到消费者估值与退货率等条件的影响。当L型消费者的估值较低、且退货率处于适中区间时，策略SH的努力水平不少于策略D，并且二者均高于策略SL。而当消费者估值较高或退货率发生变化时，努力水平会在策略D与策略SH之间切换。如果L型消费者的估值处于中等或较高水平，同时退货率偏高，且直播渠道的退货率不超过常规渠道，那么策略SH能够实现最高的努力水平；反之，则以策略D为最优。

Lemma 3.3 shows that in model R, the live streaming effort levels of the three pricing strategies have a fixed order of high and low: Strategy D is higher than Strategy SH, and Strategy SH is higher than Strategy SL. In contrast, in model A, the optimal effort level is affected by conditions such as consumer valuation and return rate. When the valuation of L-type consumers is low and the return rate is in a moderate range, the effort level of Strategy SH is no less than that of Strategy D, and both are higher than Strategy SL. When the consumer valuation is high or the return rate changes, the effort level will switch between Strategy D and Strategy SH. If the valuation of L-type consumers is at a medium or high level, the return rate is high, and the return rate of the live streaming channel does not exceed that of the regular channel, then Strategy SH can achieve the highest effort level; otherwise, Strategy D is the best.

定理3.3通过比较不同销售模式下三种定价策略的利润差异得出结论：在模式R中，供应商和平台的利润高低会受到消费者估值、退货率以及成本系数等因素的制约。当成本系数较低时，双方可能同时更偏向选择策略SH，从而形成一个均衡区间；但如果不存在消费者退货，则该均衡区间不会出现。在模式A下，供应商与平台的利润格局更加复杂，其结果依赖于估值范围、定价参数以及成本条件。在不同情况下，可能是策略SL，也可能是策略SH获得最高利润，从而成为双方的均衡选项。这说明，当引入消费者退货因素时，平台与供应商的最优定价策略会呈现动态切换，而均衡解与退货特征之间存在紧密联系。

Theorem 3.3 compares the profit differences between three pricing strategies under different sales models and concludes that in Model R, the profits of suppliers and platforms are constrained by factors such as consumer valuation, return rate, and cost coefficient. When the cost coefficient is low, both parties may simultaneously prefer strategy SH, thus forming an equilibrium range; however, if there are no consumer returns, this equilibrium range will not occur. Under Model A, the profit structure between suppliers and platforms is more complex, and the results depend on the valuation range, pricing parameters, and cost conditions. Under different circumstances, either strategy SL or strategy SH may achieve the highest profit, thus becoming the equilibrium option for both parties. This shows that when the factor of consumer returns is introduced, the optimal pricing strategies of platforms and suppliers will switch dynamically, and the equilibrium solution is closely related to the return characteristics.

表3-5与表3-6显示，当虚拟退货导致直播渠道匹配质量不确定性增加时，模式R下供应商倾向于采用策略SL，而平台更倾向策略SH。在模式A中，供应商和平台的最优定价策略呈现出更多变化：随着消费者估值区间的调整，供应商的选择逐渐从策略SH转向策略SL，平台也更频繁地采用策略SL。这表明，退货因素使双方在模式A下更偏向采取保守的定价策略。

Tables 3-5 and 3-6 show that when virtual returns increase uncertainty in the quality of live streaming channel matches, suppliers tend to adopt strategy SL in Model R, while platforms prefer strategy SH. In Model A, the optimal pricing strategies of suppliers and platforms exhibit greater variation: as consumers' valuation ranges adjust, suppliers gradually shift from strategy SH to strategy SL, and platforms also adopt strategy SL more frequently. This suggests that the factor of returns leads both parties to adopt more conservative pricing strategies in Model A.

2、模型扩展（Model extension）

（1）冲动消费引发的消费者退货（Consumer returns due to impulse buying）

数值实验结果显示，冲动消费引发的额外退货会加剧供应链利润下降，其影响趋势与质量不匹配引起的退货类似。在不同参数设置下，模式R总体上对平台更为有利，供应商在大部分情况下也倾向选择模式R。然而，当退货补贴比例较高或消费者估值区间较宽时，模式A的相对优势可能显现，从而使供应商与平台在模式选择上出现分化。

Numerical experiments show that excessive returns caused by impulse buying exacerbate supply chain profit declines, with a similar impact trend to returns caused by quality mismatch. Under different parameter settings, Model R is generally more beneficial to the platform, and suppliers generally prefer Model R. However, when the return subsidy ratio is high or the consumer valuation range is wide, the relative advantage of Model A may become apparent, leading to a divergence in model selection between suppliers and platforms.

（2）直播成本分摊（Live broadcast cost sharing）

引入成本分摊机制后，供应商与平台只有在分摊比例低于一定阈值时，才能获得非负的需求和利润。与基本模型相比，模式R与模式A下定价策略的主要结论仍然成立，说明成本分摊并未改变定价规律。在销售模式选择方面，大部分情况下策略D与策略SL的结论保持稳健，但策略SH下出现了差异化：当佣金率较低时，平台的最优模式由A转向R；而当佣金率适中且退货率偏低时，供应商的选择则从模式R转向模式A。由此可见，成本分摊机制对定价影响有限，但在特定情境下会显著调整双方的销售模式偏好，其作用主要源于分摊比例对边际退货成本承担的再分配效应。

After the introduction of the cost-sharing mechanism, suppliers and platforms can only achieve non-negative demand and profits when the cost-sharing ratio falls below a certain threshold. Compared with the basic model, the main conclusions for the pricing strategies under Model R and Model A still hold, indicating that cost-sharing does not change the pricing pattern. In terms of sales model selection, the conclusions for Strategies D and SL remain robust in most cases, but differentiation emerges under Strategy SH: when the commission rate is low, the platform's optimal model shifts from A to R; when the commission rate is moderate and the return rate is low, the supplier's choice shifts from Model R to Model A. This shows that the cost-sharing mechanism has a limited impact on pricing, but in specific situations it can significantly adjust the sales model preferences of both parties. This effect is mainly due to the redistributive effect of the cost-sharing ratio on the marginal return cost.

（3）外生佣金的情形（The case of exogenous commissions）

在外生佣金的情况下，平台先确定佣金比例，随后供应商决定直播投入。结果表明，平台通常倾向于设定较高佣金以实现自身利润最大化。在这种安排下，供应商在销售模式上更偏向自主主导，而平台则仍偏向由平台主导，这一趋势在不同定价策略下大致保持不变。仅在少数情境下，例如整体消费者估值较高或部分消费者估值较低且直播成本较低时，平台才可能选择由供应商主导的模式。进一步分析定价策略可见，供应商始终倾向高价策略，而平台则始终选择低价策略。总体来看，佣金比例内生化强化了双方在销售模式选择上的分化，但对定价策略的基本规律并未产生实质性影响。

With exogenous commissions, the platform first determines the commission rate, and the supplier then decides on the livestreaming investment. Results show that platforms generally tend to set higher commission rates to maximize their own profits. Under this arrangement, suppliers tend to be more autonomous in their sales model, while platforms still prefer a platform-led model. This trend remains largely unchanged across different pricing strategies. Only in a few situations, such as when overall consumer valuations are high or when some consumer valuations are low, and livestreaming costs are low, will the platform choose a supplier-led model. Further analysis of pricing strategies reveals that suppliers consistently favor high-price strategies, while platforms consistently choose low-price strategies. Overall, the endogenous commission rate reinforces the divergence between the two parties in their choice of sales model, but does it have a substantial impact on the underlying principles of pricing strategy.

（4）结果关于p的鲁棒性检验（Results robustness test on p）

在放宽消费者估值分布假设的情况下，我们重新设定了直播与常规渠道中不同类型消费者的比例，以更真实地反映直播对消费者估值的提升效果。数值结果显示，大多数情况下，平台与供应商的销售模式选择保持稳定，只有在少数极端情境下才会发生变化。例如，当佣金率较低、服务敏感度较高，且常规渠道中高估值消费者比例偏低，或者在部分参数组合下，平台可能会根据消费者结构调整决策；同时，供应商的选择也可能因直播效果的差异而在不同模式间切换。总体来看，即便放宽了相关假设，基础模型的核心结论依然稳健，仅在特定条件下才会出现差异。

By relaxing the assumptions about the distribution of consumer valuations, we reset the proportions of different types of consumers in live streaming and conventional channels to more realistically reflect the effect of live streaming on consumer valuations. Numerical results show that in most cases, the sales model choices of platforms and suppliers remain stable, and only change in a few extreme scenarios. For example, when the commission rate is low, service sensitivity is high, and the proportion of high-valuation consumers in conventional channels is low, or under certain parameter combinations, the platform may adjust its decision based on the consumer structure; at the same time, the supplier's choice may switch between different models due to differences in live streaming effects. Overall, even if the relevant assumptions are relaxed, the core conclusions of the basic model remain robust, and differences only appear under specific conditions.

（5）结果关于消费者估值的鲁棒性检验（Results robustness test on consumer valuation）

在基本模型中，最初假设仅部分低估值消费者因直播而转化为高估值消费者。为检验该设定的合理性，进一步将消费者划分为三类：高估值、因直播提升至中等估值，以及估值未改善的低估值。分析结果表明，这一细分对大多数结论并无影响。在策略D下，尽管需要考虑最低估值消费者，销售模式选择仍保持不变。仅在极端情形下，如果所有低估值消费者都转化为高估值或中等估值消费者，定价策略才会出现差异。数值结果显示，此时策略D的优势增强，尤其当中等估值消费者比例较高时，平台更倾向选择策略D。总体来看，消费者估值的改善不会动摇销售模式选择的稳定性，但在特殊条件下会促使定价策略向策略D倾斜。

In the basic model, the initial assumption is that only a portion of low-valued consumers are converted to high-valued consumers due to live streaming. To test the rationale of this assumption, consumers are further divided into three categories: high-valued, those whose valuations are improved to medium due to live streaming, and low-valued consumers whose valuations do not improve. The analysis shows that this segmentation has no impact on most conclusions. Under Strategy D, despite the need to consider the lowest-valued consumers, the choice of sales model remains unchanged. Only in the extreme case, if all low-valued consumers are converted to high-valued or medium-valued consumers, will the pricing strategy differ. Numerical results show that in this case, the advantage of Strategy D is enhanced, especially when the proportion of medium-valued consumers is high, in which case the platform is more inclined to choose Strategy D. Overall, improvements in consumer valuations do not affect the stability of sales model selection, but under special circumstances, they can cause pricing strategies to shift towards Strategy D.

（6）考虑残值的鲁棒性检验（Robustness test considering residual value）

在引入残值回收机制后，虽然批发价格和市场定价有所调整，但供应商与平台在销售模式和定价策略上的整体选择趋势保持稳定。具体来看，多数情况下供应商仍倾向以直播为主的销售模式，而平台则更偏好传统渠道为主，这一差异主要源于平台设定较高佣金率所带来的收益分配效果。仅在消费者估值较低、市场规模有限且直播成本偏低的情况下，平台才可能转向选择直播模式。在定价策略方面，供应商始终倾向高价以保障利润，而平台则偏好低价策略以扩大市场需求。总体而言，残值回收机制并未改变双方博弈的稳定选择格局，但对利润水平和收益分配具有一定调节作用。

After the introduction of the residual value recovery mechanism, although wholesale prices and market pricing have adjusted, the overall trend of suppliers and platforms in choosing sales models and pricing strategies has remained stable. Specifically, in most cases, suppliers still prefer a sales model based on live streaming, while platforms prefer traditional channels. This difference is mainly due to the profit distribution effect brought about by the higher commission rates set by platforms. Only when consumer valuations are low, the market size is limited, and the cost of live streaming is relatively low, will platforms turn to the live streaming model. In terms of pricing strategy, suppliers always tend to set high prices to protect profits, while platforms prefer low-price strategies to expand market demand. Overall, the residual value recovery mechanism has not changed the stable choice pattern of the game between the two parties, but it has a certain regulatory effect on profit levels and profit distribution.

三、知识补充（Knowledge supplementation）

1、鲁棒性的定义（Definition of robustness）

鲁棒性通常指系统在面对内部结构变化或外部环境干扰时，仍能够维持功能稳定运行的能力。该特性广泛应用于计算机科学、控制工程、生物学以及数学模型等多个领域，但在不同领域中的具体含义略有差异。例如，在计算机软件中，鲁棒性指软件在面对输入错误、磁盘故障、网络过载或恶意攻击时，仍能正常运行、不崩溃、不死机；在控制系统中，鲁棒性表示系统在参数存在一定幅度扰动时，仍能保持某些性能指标；而在生物系统中，当细胞遭遇环境变化或遗传变异时，其能否正常存活并发挥生物功能，即体现了该细胞系统的鲁棒性。

Robustness generally refers to the ability of a system to maintain stable functional operation in the face of changes in its internal structure or external environmental interference. This characteristic is widely used in many fields, including computer science, control engineering, biology, and mathematical modeling, but its specific meaning varies slightly in different fields. For example, in computer software, robustness refers to the ability of the software to continue to operate normally without crashing or freezing in the face of input errors, disk failures, network overloads, or malicious attacks; in control systems, robustness means that the system can still maintain certain performance indicators when there are certain amplitude disturbances in the parameters; and in biological systems, when cells encounter environmental changes or genetic mutations, their ability to survive normally and perform biological functions reflects the robustness of the cell system.

2、鲁棒性检验概述（Overview of robustness testing）

鲁棒性检验是一种评估方法，用于测试系统在不完美或异常条件下的表现。其主要目的是检验系统应对无效输入、异常数据、错误情况或外部干扰的能力。通过鲁棒性检验，可以了解系统在现实环境中运行的稳定性和可靠性，并发现潜在的弱点、边界条件以及漏洞，从而提升系统的整体性能和稳健性。为了确保系统在实际应用中能够正确处理各种情况并实现恢复，测试应根据具体应用场景和系统需求进行针对性设计。

Robustness testing is an evaluation method used to test a system's performance under imperfect or abnormal conditions. Its primary purpose is to verify the system's ability to cope with invalid inputs, abnormal data, error conditions, or external interference. Robustness testing can help understand the stability and reliability of a system in real-world environments and identify potential weaknesses, boundary conditions, and vulnerabilities, thereby improving the system's overall performance and robustness. To ensure that the system can correctly handle and recover from various situations in real-world applications, testing should be tailored to the specific application scenario and system requirements.

3、鲁棒性检验时通常考虑的方面（Aspects commonly considered in robustness testing）

（1）无效输入测试（Invalid input test）

测试系统对非预期或无效输入的响应能力，包括输入为空、格式错误、数值越界或包含非法字符等情况。

Test the system's ability to respond to unexpected or invalid input, including input that is empty, malformed, out of range, or contains illegal characters.

（2）异常数据测试（Abnormal data testing）

测试系统在面对异常或罕见数据时的处理能力，包括异常值、异常数据分布以及数据不完整等情况。

Test the system's ability to handle unusual or rare data, including outliers, unusual data distributions, and incomplete data.

（3）边界条件测试（Boundary condition testing）

测试系统在边界值条件下的表现，包括系统在接近最小值、最大值或极限值时的响应能力和稳定性。

Test the system's performance under boundary conditions, including the system's responsiveness and stability when approaching minimum, maximum, or extreme values.

（4）错误处理测试（Error handling tests）

测试系统在出现错误条件时的处理能力，例如在网络故障、数据库异常或资源不足等情况下的响应和行为。

Test the system's ability to handle error conditions, such as its response and behavior in the event of a network failure, database anomalies, or insufficient resources.

（5）干扰测试（Interference test）

测试系统在面对外部干扰时的鲁棒性，包括网络延迟、噪声干扰或其他干扰信号对系统运行的影响。

Test the system's robustness in the face of external interference, including the impact of network delays, noise interference, or other interfering signals on system operation.

（6）异常流程测试（Abnormal process testing）

测试系统在处理非正常或异常流程时的表现，包括在中断、中止或重启等情况下的恢复能力和稳定性。

Test the system's performance when handling abnormal or exceptional processes, including its recovery and stability in the event of interruptions, suspensions, or restarts.

（7）兼容性测试（Compatibility testing）

测试系统在不同操作系统、浏览器、设备或运行环境下的兼容性和交互性能。

Test the system's compatibility and interactive performance under different operating systems, browsers, devices or operating environments.

（8）安全性测试（Security testing）

测试系统在面对安全攻击、恶意输入或漏洞利用时的鲁棒性及防护能力。

Test the system's robustness and protection against security attacks, malicious input, or vulnerability exploits.

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