慧学（39）：精读博士论文代销模式下平台广告和推广策略（2）

摘要：In this issue, the editor will introduce the platform advertising and targeted promotion strategies under the agency sales model (

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“慧学（39）：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》代理销售模式下平台广告和定向推广策略（2）”

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"Hui Xue (39): Intensive reading of doctoral dissertation

'Optimization of Platform Supply Chain Sales Strategies Based on Consumer behavior' platform advertising and targeted promotion strategies under the agency sales model (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》代理销售模式下平台广告和定向推广策略（2）。

In this issue, the editor will introduce the platform advertising and targeted promotion strategies under the agency sales model (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、模型比较与分析（Model comparison and analysis）

（1）广告模式比较（Advertising model comparison）

根据定理4.3，在未采用定向推广时，平台在付费广告模式下的投入与收益均超过免费广告模式，这意味着平台整体更偏好付费广告。从商家的角度看，其最优策略与参数大小密切相关。当参数值较低时，平台并不分担广告开支，商家需独自承担全部广告费用，但因需求增加和佣金下降，其在付费广告模式中的利润仍更高。相反，当参数值较高时，平台会分摊部分广告支出，虽然需求有所增长，但商家需额外负担部分费用并支付更高佣金，导致利润下降。由此可见，平台始终倾向选择付费广告，而商家则会根据参数区间作出不同选择。

According to Theorem 4.3, when targeted promotion is not employed, the platform's investment and revenue under the paid advertising model exceed those under the free advertising model, meaning that the platform generally prefers paid advertising. From the merchant's perspective, the optimal strategy is closely related to the parameter size. When the parameter value is low, the platform does not share advertising expenses, and merchants bear the entire advertising cost. However, due to increased demand and lower commissions, their profits under the paid advertising model are still higher. Conversely, when the parameter value is high, the platform shares some advertising expenses. Although demand increases, merchants have to bear some additional costs and pay higher commissions, resulting in lower profits. This shows that platforms consistently prefer paid advertising, while merchants make different choices depending on the parameter range.

定理4.4指出，在存在定向推广的情形下，采用付费广告并结合定向推广时，平台在广告投入、推广强度以及利润方面均超过免费广告加定向推广的模式，这与定理4.3的结论相一致，表明定向推广并未改变平台对付费广告的偏好。对商家而言，其收益受到参数水平和推广成本的共同影响。当参数处于较低水平时，付费广告结合定向推广能够带来更高利润；然而，当参数较高且推广费用过大时，平台在推广强度上的提升有限，商家反而可能在免费广告加定向推广模式下获得更优回报。由此可见，在定向推广环境中，平台与商家之间可能出现多种均衡状态，广告费用的分担也可能因此成为现实。

Theorem 4.4 states that, in the presence of targeted promotion, when paid advertising is combined with targeted promotion, the platform outperforms the free advertising plus targeted promotion model in terms of advertising investment, promotion intensity, and profit. This is consistent with the conclusion of Theorem 4.3, indicating that targeted promotion has not changed the platform's preference for paid advertising. For merchants, their profits are influenced by both the parameter level and promotion costs. When the parameter is low, the combination of paid advertising and targeted promotion can generate higher profits; however, when the parameter is high and the promotion cost is excessive, the platform's improvement in promotion intensity is limited, and merchants may instead obtain better returns with free advertising plus targeted promotion. This shows that in a targeted promotion environment, multipleequilibrium states can emerge between the platform and merchants, and the sharing of advertising costs can become a reality.

命题4.2进一步表明，佣金率的上升往往会削弱付费广告模式的优势。随着佣金提高，商家会缩减广告支出，进而引发需求下降，迫使平台不得不增加广告分担或投入更多推广成本。虽然佣金收入有所增加，但整体费用也随之上升。相比之下，在付费广告结合定向推广的模式下，较高佣金率带来的负面效应能够被定向推广的正向外溢作用部分抵消，使商家依然愿意增加广告投入，从而使平台和商家双方都有可能获得更高收益。

Proposition 4.2 further suggests that rising commission rates tend to weaken the advantages of the paid advertising model. As commissions rise, merchants will reduce advertising spending, which in turn leads to a decline in demand, forcing the platform to increase its advertising share or invest more in promotional costs. While commission revenue increases, overall expenses also rise. In contrast, in a model combining paid advertising with targeted promotion, the negative effects of higher commission rates are partially offset by the positive spillover effects of targeted promotion, encouraging merchants to continue to increase advertising investment, thereby potentially generating higher returns for both the platform and merchants.

图4-4的结果表明，无论是否引入定向推广，平台在付费广告模式下的利润始终高于免费广告模式。当佣金率为正时，两种模式之间的利润差距会随佣金率上升而不断扩大；而当佣金率为负时，差距则会随着其绝对值增加而逐渐缩小。图4-5进一步显示，商家在付费广告模式下的收益可能高于或低于免费广告模式，具体取决于参数与佣金率的组合。当参数处于中间区间时，商家的利润差距可能转为负值，即免费广告模式更具优势。然而，在付费广告叠加定向推广的情境中，高佣金率下商家的利润差距会随参数上升而扩大；相反，当佣金率为负且绝对值较大时，付费广告模式反而表现出更强优势，因为在免费广告模式下，平台广告可能挤压线下销售，对商家造成更大损失。总体而言，平台在任何条件下都偏好付费广告，而商家的最优选择则受到参数水平、推广开支和佣金率等多重因素的影响。

The results in Figure 4-4 show that, regardless of whether targeted promotion is implemented, platforms consistently achieve higher profits under the paid advertising model than under the free advertising model. When the commission rate is positive, the profit gap between the two models widens as the commission rate increases; when the commission rate is negative, the gap narrows as its absolute value increases. Figure 4-5 further demonstrates that merchants' profits under the paid advertising model can be higher or lower than those under the free advertising model, depending on the combination of parameters and commission rate. When the parameters are in the middle range, the profit gap for merchants can turn negative, indicating that the free advertising model has a greater advantage. However, in the scenario of combining paid advertising with targeted promotion, the profit gap for merchants under high commission rates widens as the parameters increase. Conversely, when the commission rate is negative and large in absolute value, the paid advertising model exhibits a stronger advantage because, under the free advertising model, platform advertising may squeeze offline sales, resulting in greater losses for merchants. Overall, platforms prefer paid advertising under all conditions, while merchants' optimal choice is influenced by multiple factors, including parameter settings, promotion expenditures, and commission rate.

（2）模式选择（Mode selection）

命题4.3的结论显示，在四种广告模式的比较中，平台始终更偏向于付费广告结合定向推广的模式，因为这一方案能够使其利润最大化。相比之下，商家的注册选择则受到佣金率和推广成本的共同影响。当二者水平较低时，商家在采用付费广告加定向推广的平台上入驻最为有利。此时，商家的广告投入会推动平台加大推广力度，从而提升广告效果并带来更高回报，即便存在线上广告对线下销售的挤压效应，该结论依然成立。然而，当佣金率和推广成本处于较高水平时，平台在推广方面的努力相对有限，商家分担广告费用的优势不复存在，此时选择注册在提供免费广告加定向推广模式的平台上反而更为合理，如图4-6所示。

The conclusion of Proposition 4.3 shows that, when comparing the four advertising models, platforms consistently prefer a model that combines paid advertising with targeted promotion because it maximizes their profits. In contrast, merchants' registration choices are influenced by both commission rates and promotion costs. When both are low, merchants are most advantageous on platforms that employ paid advertising and targeted promotion. In this scenario, merchants' advertising investment drives platforms to increase their promotional efforts, thereby improving advertising effectiveness and generating higher returns. This conclusion holds true even when online advertising squeezes offline sales. However, when commission rates and promotion costs are high, platforms' promotional efforts are relatively limited, and the advantage of merchants sharing advertising costs disappears. In this case, registering on platforms that offer free advertising and targeted promotion is more reasonable, as shown in Figure 4-6.

2、定向推广的成本分摊（Cost sharing for targeted promotion）

（1）导语（Introduction）

在第4.1节和第4.2节中，已分析了广告费用由平台或商家分摊的情况，并假设定向推广成本由平台承担。但在现实中，消费者数据和推广均由平台掌握，商家同样受益，因此由其分担成本更为合理。例如，淘宝直通车中有平台统一定价的“闪卖”模式，对应内生分摊比例；也有商家通过竞价决定费用的模式，对应外生分摊比例。基于此，本节将定向推广成本分摊纳入模型，分别讨论免费广告和付费广告模式，并用分摊比例刻画平台与商家的成本分担关系，从而揭示利润函数随分摊比例变化的规律，为实际成本分配提供参考。

In Sections 4.1 and 4.2, we analyzed the scenarios where advertising costs are shared by the platform or by merchants, assuming that the platform bears the costs of targeted promotion. However, in reality, platforms control both consumer data and promotions, benefiting merchants equally. Therefore, it is more reasonable for them to share the costs. For example, Taobao Direct Express offers a "flash sale" model where the platform sets unified pricing, corresponding to an endogenous cost sharing ratio; there are also models where merchants determine their costs through bidding, corresponding to an exogenous cost sharing ratio. Based on this, this section incorporates the cost sharing of targeted promotion into the model, discussing both free and paid advertising models. We use the cost sharing ratio to characterize the cost sharing relationship between the platform and merchants, thereby revealing how the profit function changes with the cost sharing ratio, providing a reference for actual cost allocation.

（2）内生的分摊比例（Endogenous allocation ratio）

在内生分摊比例机制下，随着分摊比例的上升，平台的利润呈下降趋势，因此最优选择是由商家独自承担全部定向推广费用。换言之，平台通常依靠转嫁成本来获取收益，而这必然会损害商家的利益。这一结论与现实相符，例如在淘宝直通车的“闪卖”模式中，平台通过设置较高的价格，使商家承担全部推广开支，并主要用于热门商品的宣传。与广告支出不同的是，广告费用的内生分配有可能带来平台和商家双方共赢，但定向推广成本并不具备这种均衡性。基于这一差异，下一部分将转向外生分摊比例的讨论，以寻求一种能让双方共同获益的解决思路。

Under an endogenous sharing ratio mechanism, as the sharing ratio increases, the platform's profits decline. Therefore, the optimal option is for merchants to bear all targeted promotion costs. In other words, platforms often rely on cost shifting to generate revenue, which inevitably harms merchants' interests. This conclusion aligns with reality. For example, in Taobao's "flash sale" model, the platform sets higher prices, forcing merchants to bear all promotional expenses, primarily for promoting popular products. Unlike advertising expenditures, the endogenous allocation of advertising costs can result in a win-win situation for both platforms and merchants, but targeted promotion costs do not offer this equilibrium. Based on this difference, the next section will turn to the discussion of exogenous sharing ratios, seeking a solution that benefits both parties.

（3）外生的分摊比例（Exogenous allocation ratio）

在外生分摊比例的情况下，定向推广费用的分担由市场机制决定，而非由平台单方面设定。根据引理4.5，为了确保模型解的合理性，需要对分摊比例的取值范围进行约束。在这一条件下，分析结果显示，广告费用的分摊只有在比例适中时才能发挥正向作用，从而激励商家持续投入广告，并推动平台加大定向推广力度。因此，假设平台设定外生分摊比例不仅合理，也为双方的策略选择提供了理论依据。

In the case of an exogenous sharing ratio, the sharing of targeted promotion costs is determined by market mechanisms, rather than unilaterally set by the platform. According to Lemma 4.5, to ensure the rationality of the model solution, it is necessary to constrain the range of the sharing ratio. Under this condition, the analysis results show that the sharing of advertising costs can only have a positive effect when the ratio is moderate, thereby incentivizing merchants to continue investing in advertising and prompting the platform to increase its targeted promotion efforts. Therefore, the assumption that the platform sets an exogenous sharing ratio is not only reasonable but also provides a theoretical basis for the strategic choices of both parties.

在定理4.5的进一步比较中可见，在免费广告模式下，适度的外生分摊比例能够提升平台和商家的最优利润。商家在承担部分成本后仍可能获得更高回报，这是因为平台在分担部分费用后，会加大定向推广投入，从而提高广告效果。然而，需要注意的是，当佣金率或分摊比例过高时，商家的利润可能下降，甚至低于未分摊时的水平。图4-7展示了在不同参数组合下，免费广告模式中平台与商家利润差随分摊比例和佣金率变化的情况，直观地反映了这种临界效应。

Further comparison with Theorem 4.5 shows that, under the free advertising model, a moderate exogenous sharing ratio can improve the optimal profits of both the platform and merchants. Merchants can still achieve higher returns even after bearing some of the costs. This is because, after sharing some of the costs, the platform will increase its investment in targeted promotion, thereby improving advertising effectiveness. However, it is important to note that when the commission rate or sharing ratio is too high, merchants' profits may decline, even falling below the level without sharing. Figure 4-7 shows how the profit differential between the platform and merchants in the free advertising model changes with the sharing ratio and commission rate under different parameter combinations, visually demonstrating this critical effect.

在付费广告模式下，商家的行为更为复杂。图4-8和图4-9显示，当商家本身已承担广告费用时，额外分摊定向推广成本会增加其负担。此时，商家利润提升的空间有限，甚至在临界条件下可能无法从分摊机制中获益。这表明，在PT模式下，分摊定向推广成本较难实现双方共赢。因此，尽管外生分摊比例在理论上有助于平台与商家合作，其适用性在不同模式下存在差异：在免费广告模式中，合理的分摊比例更易实现双赢；而在付费广告模式中，商家的承受能力受到限制，使该机制的优势相对减弱。

Under the paid advertising model, merchants' behavior is more complex. Figures 4-8 and 4-9 show that when merchants already bear advertising costs, sharing the additional costs of targeted promotion increases their burden. In this scenario, merchants have limited room for profit growth, and under critical conditions, they may not even benefit from the sharing mechanism. This suggests that under the PT model, sharing the costs of targeted promotion is less likely to achieve a win-win situation for both parties. Therefore, while an exogenous sharing ratio theoretically facilitates cooperation between platforms and merchants, its applicability varies across different models: in free advertising models, a reasonable sharing ratio is more likely to achieve a win-win situation; in paid advertising models, however, merchants' affordability is limited, which reduces the advantages of this mechanism.

三、知识补充（Knowledge supplementation）

1、分摊比例概述（Overview of the allocation ratio）

分摊比例是指根据特定标准，例如面积、使用频率或受益程度，将费用、资源或损失按比例分配给相关方的一种经济学方法。其核心在于通过量化的分配机制实现公平性，广泛应用于房产管理、保险赔偿以及企业成本核算等领域。在具体操作中，需要依据使用面积、受益程度或事先约定的比例进行计算。虽然该方法操作简便，但在涉及因素复杂或各方贡献不均的情况下，应结合其他方法进行调整，以确保分配的合理性。

The apportionment ratio is an economic method that allocates expenses, resources, or losses proportionally to relevant parties based on specific criteria, such as area, frequency of use, or degree of benefit. Its core principle is to achieve fairness through a quantitative allocation mechanism. It is widely used in fields such as real estate management, insurance compensation, and corporate cost accounting. In practice, calculations are based on area used, degree of benefit, or a pre-agreed ratio. While this method is simple to implement, when complex factors are involved or contributions are uneven, it should be combined with other methods to ensure fair distribution.

2、内生变量和外生变量（Endogenous and exogenous variables）

在经济模型中，内生变量是指由模型内部决定的变量，其取值可以通过模型体系中的关系加以解释和确定；而外生变量则由模型外部的因素决定，是模型建立所依赖的已知条件，本身不能在模型体系内得到说明。通常，参数也由模型外部因素确定，因此往往被视为外生变量。例如，在经济增长模型中，投资属于内生变量，因为它由利率、收入等因素决定；而政府政策如税收政策属于外生变量，因为其设定来源于模型之外。总的来说，内生变量由模型内部生成和解释，外生变量则由模型外部提供。

In economic models, endogenous variables are those determined internally by the model, whose values can be explained and determined by the relationships within the model system. Exogenous variables, on the other hand, are determined by factors external to the model and are known conditions upon which the model is built, but cannot themselves be explained within the model system. Parameters are often determined by factors external to the model and are therefore often considered exogenous variables. For example, in an economic growth model, investment is an endogenous variable because it is determined by factors such as interest rates and income; whereas government policies, such as tax policy, are exogenous variables because their settings originate outside the model. In general, endogenous variables are generated and explained within the model, while exogenous variables are provided by factors external to the model.

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翻译：Google翻译

参考资料：百度、Chatgpt