慧学（42）：精读博士论文考虑消费者情绪的平台裂变营销（1）

摘要：In this issue, the editor will introduce the platform fission marketing that considers consumer emotions (1) of the doctoral disse

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“慧学（42）：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》考虑消费者情绪的平台裂变营销（1）”

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”Hui Xue (42): Intensive reading of doctoral dissertation ‘Optimization of Platform Supply Chain Sales Strategies Based on Consumer behavior’ platform fission marketing that considers consumer emotions （1）”

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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》考虑消费者情绪的平台裂变营销（1）。

In this issue, the editor will introduce the platform fission marketing that considers consumer emotions (1) 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、引言（Introduction）

本章研究电商平台在裂变营销中的运营选择。裂变营销分为口碑型和折扣型：前者依赖产品声誉和用户心理需求（如Keep的运动分享），后者通过价格优惠促进传播（如拼多多、瑞幸）。实践中，有的企业采取深度裂变，有的选择适度甚至放弃，这既与成本相关，也因裂变营销不同于传统广告。折扣虽能吸引用户，但也可能带来社交压力和声誉风险，因此本章重点考察消费者偏好与厌恶对决策的影响。研究关注三点：（1）平台何时采用裂变营销；（2）不同模式下如何确定力度；（3）消费者偏好与厌恶如何作用于决策。相比团购或推荐奖励，本文贡献在于：第一，裂变营销在分享时即可获得折扣，不依赖接收方购买；第二，它是购买前的单阶段机制，新老用户均可参与；第三，现有研究忽视其社交属性与负面情绪。本研究既考虑了积极和消极情绪，也比较了深度与适度裂变，填补了相关空白。

This chapter studies the operational choices of e-commerce platforms in fission marketing. Fission marketing is divided into word-of-mouth and discount types: the former relies on product reputation and user psychological needs (such as Keep's sports sharing), while the latter promotes dissemination through price discounts (such as Pinduoduo and Luckin Coffee). In practice, some companies adopt deep fission, while others choose moderate or even give up. This is related to both cost and the fact that fission marketing is different from traditional advertising. Although discounts can attract users, they may also bring social pressure and reputation risks. Therefore, this chapter focuses on the impact of consumer preferences and aversions on decision-making. The research focuses on three points: (1) when the platform adopts fission marketing; (2) how to determine the intensity under different models; and (3) how consumer preferences and aversions affect decision-making. Compared with group buying or recommendation rewards, the contribution of this paper is: first, fission marketing can obtain discounts when sharing, and does not rely on the recipient to purchase; second, it is a single-stage mechanism before purchase, and both new and old users can participate; third, existing research ignores its social attributes and negative emotions. This study considers both positive and negative emotions and compares deep and moderate fission, filling the relevant gaps.

2、模型和均衡结果（Model and equilibrium results）

（1）导语（Introduction）

本章通过模型构建，探讨电商平台在初始市场与社交媒体市场中的裂变营销选择。对于口碑裂变，平台先设定裂变强度与投入水平，再由消费者决定购买与否；在折扣裂变中，平台除了确定裂变程度，还需进一步选择营销投入和折扣价格。假定消费者估值在区间[0,1]上均匀分布，社交媒体用户已掌握产品信息，因此裂变营销的主要功能是促进购买。基准情境下，若无裂变营销，产品以固定价格出售，平台利润来自两个市场。与传统广告不同，裂变营销可能引发积极或消极情绪，消费者被划分为偏好型与厌恶型，两类比例保持不变，情绪影响强度由敏感系数衡量。在折扣裂变下，消费者按照折扣价格购买。为便于后续分析，本章进一步给出了估值、市场规模、价格、成本、消费者比例、需求、效用与利润等变量的定义。

This chapter explores the fission marketing options of e-commerce platforms in both the initial and social media markets through model construction. For word-of-mouth fission, the platform first sets the fission intensity and investment level, and then consumers decide whether to purchase. In discount fission, in addition to determining the fission level, the platform must further select marketing investment and discount prices. Assuming that consumer valuations are uniformly distributed on the interval [0, 1] and that social media users already possess product information, the primary function of fission marketing is to promote purchases. In the baseline scenario, without fission marketing, products are sold at a fixed price, and the platform's profits derive from both markets. Unlike traditional advertising, fission marketing can elicit positive or negative emotions, categorizing consumers into those who favor or dislike the product, with the proportion of these two categories remaining constant. The intensity of the emotional impact is measured by the sensitivity coefficient. Under discount fission, consumers purchase at the discounted price. To facilitate subsequent analysis, this chapter further defines variables such as valuation, market size, price, cost, consumer proportion, demand, utility, and profit.

（2）口碑裂变营销（Word-of-mouth fission marketing）

1）适度口碑营销（Moderate word-of-mouth marketing）

在适度口碑裂变的情境下，平台在社交媒体上实施裂变营销时，需要保证偏好型与厌恶型消费者的预期效用均不为负。在模型推导过程中发现，若均衡解中的营销努力为负，则与现实情况不符，因此取边界解为零，仅考虑偏好型消费者需求的有效部分。在该模型下，平台利润由四部分组成：初始市场的销售收益、社交媒体上偏好型消费者的销售利润、社交媒体上厌恶型消费者的销售利润，以及裂变营销所需的成本支出。为了保证均衡解具备现实意义，研究提出三项假设：第一，产品价格必须高于成本且低于最大估值，以确保既能激励销售又能吸引消费者；第二，偏好型消费者的比例需超过一定阈值，否则裂变营销的收益不足以弥补成本；第三，裂变营销成本系数设有下限，以避免平台无限增加营销努力而导致需求超过市场容量的非合理结果。

In the context of moderate word-of-mouth fission, platforms implementing fission marketing on social media must ensure that the expected utility of both favorable and unfavorable consumers is not negative. During model derivation, it was found that a negative marketing effort in the equilibrium solution would be inconsistent with reality. Therefore, the boundary solution was set to zero, considering only the effective portion of demand from favorable consumers. In this model, platform profits are composed of four components: sales revenue in the initial market, sales profits from favorable consumers on social media, sales profits from unfavorable consumers on social media, and the costs of fission marketing. To ensure the practicality of the equilibrium solution, the study proposes three assumptions: First, product prices must be above cost and below maximum valuation to ensure both sales incentives and consumer attraction; second, the proportion of favorable consumers must exceed a certain threshold; otherwise, the benefits of fission marketing will not be sufficient to offset the costs; and third, a lower bound is imposed on the fission marketing cost coefficient to prevent the platform from indefinitely increasing marketing efforts, leading to an unreasonable situation where demand exceeds market capacity.

2）深度口碑营销（In-depth word-of-mouth marketing）

在深度裂变营销情境下，由于覆盖范围更广、频率更高，厌恶型消费者的效用转为负值并选择退出，平台因此放弃该群体，仅将偏好型消费者作为目标对象。此时，需求完全来自偏好型消费者，而厌恶型消费者的需求为零。平台利润由三部分构成：产品销售收益、裂变营销带来的额外需求，以及裂变营销的投入成本。同时，平台的决策受到两类约束：其一，价格必须超过某一阈值，才能激励平台开展裂变营销；其二，裂变营销成本存在上限，当支出过高时，裂变力度受到抑制，深度裂变将无法实施。

In the context of deep fission marketing, due to the wider coverage and higher frequency, the utility of averse consumers turns negative and they choose to withdraw. The platform therefore abandons this group and targets only preferred consumers. In this case, demand comes entirely from preferred consumers, while demand from averse consumers is zero. The platform's profit is composed of three parts: product sales revenue, the additional demand generated by fission marketing, and the investment costs of fission marketing. At the same time, the platform's decision-making is subject to two types of constraints: first, the price must exceed a certain threshold to incentivize the platform to engage in fission marketing; second, there is an upper limit on the cost of fission marketing. When the expenditure is too high, the fission effect is suppressed, and deep fission will become impossible.

3）均衡解和利润（Equilibrium solution and profit）

在引理5.1中，RM模型下的最优裂变营销努力与利润同时受到积极与消极情绪、产品价格、生产成本、消费者比例以及营销成本系数等因素的影响，而RE模型的最优解仅依赖于积极情绪及其相关变量。推论5.1指出，积极情绪的增强有助于提高裂变力度和平台利润，而消极情绪则会抑制裂变并减少偏好型消费者的需求；其对厌恶型需求的作用取决于该类消费者在市场中的比例。价格因素在营销成本较低时能够提升利润，但在成本水平较高时则会对利润产生抑制。进一步地，推论5.2表明，在RE模型中，价格上升会减少偏好型需求，而利润的变化则依赖于价格与成本的相对关系：若成本过高，利润随之下降，否则可能出现增长。

In Lemma 5.1, the optimal fission marketing effort and profit under the RM model are influenced by factors such as positive and negative emotions, product price, production cost, consumer proportion, and marketing cost coefficient, while the optimal solution of the RE model depends solely on positive emotions and their related variables. Corollary 5.1 states that increased positive emotions help improve fission efforts and platform profits, while negative emotions inhibit fission and reduce demand from preferred consumers; its effect on aversion demand depends on the proportion of such consumers in the market. Price factors can increase profits when marketing costs are low, but they can suppress profits when costs are high. Furthermore, Corollary 5.2 shows that in the RE model, price increases reduce preferred demand, while changes in profits depend on the relative relationship between price and cost: if costs are too high, profits will decline; otherwise, they may increase.

（3）折扣裂变营销（Discount fission marketing）

1）适度折扣营销（Moderate discount marketing）

在适度折扣裂变中，平台通过降低销售价格来推动营销。此时，偏好型与厌恶型消费者的效用函数均受到折扣幅度和裂变努力的影响，从而推导出两类消费者的需求函数。平台的利润由三部分组成：产品销售收益、折扣价格下形成的需求，以及裂变营销所需的成本。为了保证模型的可行性，需要满足以下约束：第一，折扣幅度不能过大，否则平台将难以保持盈利；第二，营销成本必须高于一定门槛，以确保需求为正且不超过市场规模；第三，偏好型消费者比例需高于某一阈值，否则可能出现无效均衡甚至负的解。

In moderate discount fission, the platform promotes marketing by lowering sales prices. In this case, the utility functions of both favoring and averse consumers are affected by the discount magnitude and fission effort, thus deriving the demand functions of the two types of consumers. The platform's profit is composed of three components: product sales revenue, demand generated at the discounted price, and the costs of fission marketing. To ensure the feasibility of the model, the following constraints must be met: First, the discount magnitude cannot be too large, otherwise the platform will find it difficult to maintain profitability; second, marketing costs must be above a certain threshold to ensure positive demand and do not exceed market size; third, the proportion of favoring consumers must be above a certain threshold, otherwise an invalid equilibrium or even a negative solution may occur.

2）深度折扣营销（Deep discount marketing）

在深度折扣裂变情境下，平台会加大营销投入，使厌恶型消费者的效用降为负值并退出市场，因而需求仅来自偏好型群体。此时，平台的利润来源包括三部分：产品销售收益、偏好型消费者在折扣价格下的需求，以及裂变营销的投入成本。为了保证模型具备可行性，需要满足以下假设：第一，裂变营销成本不能过低，否则无法维持深度裂变的实施；第二，产品价格必须保持在较高水平，以应对市场规模缩减带来的影响；第三，营销成本需设定上限，以确保厌恶型消费者的效用维持在非正状态。

In the deep discount fission scenario, the platform will increase marketing investment, causing the utility of averse consumers to drop to negative values and exit the market, so that demand only comes from the preferred group. In this case, the platform's profit comes from three sources: product sales revenue, demand from preferred consumers at discounted prices, and the investment costs of fission marketing. To ensure the feasibility of the model, the following assumptions must be met: First, the cost of fission marketing cannot be too low, otherwise the implementation of deep fission cannot be sustained; second, product prices must be maintained at a high level to cope with the impact of market size reduction; third, marketing costs must be capped to ensure that the utility of averse consumers remains non-positive.

3）均衡解和利润（Equilibrium solution and profit）

引理5.2表明，在DM与DE两类模型中均能得到最优决策与利润。DM模型下，销售价格上升会带来更高的价格折扣，最优努力和利润受到积极情绪、消极情绪、偏好型比例及成本等因素的影响；而在DE模型中，结果不受消极情绪影响，仅取决于积极情绪与偏好型比例。推论5.3进一步指出，在DM模型中，积极情绪和偏好型比例的提升能够同时增加折扣、努力和利润；而消极情绪在不同条件下可能推动或抑制厌恶型消费者的需求。总体而言，DM的结果更为复杂，而DE的结论相对简洁。

Lemma 5.2 shows that optimal decisions and profits are achieved in both the DM and DE models. In the DM model, an increase in sales price leads to a higher price discount, and optimal effort and profit are influenced by factors such as positive emotion, negative emotion, preference ratio, and cost. In the DE model, however, the results are unaffected by negative emotion and depend solely on positive emotion and preference ratio. Corollary 5.3 further indicates that in the DM model, increases in positive emotion and preference ratio can simultaneously increase discounts, effort, and profit; whereas negative emotion can, under different conditions, either boost or suppress demand from averse consumers. Overall, the DM results are more complex, while the DE conclusions are relatively concise.

三、知识补充（Knowledge supplementation）

1、内生价格概述（Overview of endogenous prices）

市场价格是由供求双方通过自由交易形成的，本质上属于内生价格，即在市场内部通过竞争而确定的价格。换言之，价格由供求关系决定：在供给保持不变的情况下，需求增加会推动价格上升；而在需求不变时，供给增加则会使价格下降。

Market prices are formed through the free exchange of supply and demand. They are essentially endogenous prices, determined through competition within the market. In other words, prices are determined by supply and demand: if supply remains unchanged, an increase in demand will drive prices up; if demand remains unchanged, an increase in supply will cause prices to fall.

2、霍特林模型概述（Overview of the hotelling model）

霍特林模型由经济学家哈罗德·霍特林于1929年提出，是用于分析双寡头市场价格稳定性的经典框架。该模型基于空间竞争理论，对埃奇沃思模型所强调的市场不稳定性提出了修正，指出产品差异化能够减弱价格竞争，从而使企业通过定价调整或产品特性改进建立市场壁垒。模型假设消费者偏好均匀分布在区间[0,1]上，两家企业分布在线段的不同位置，消费者会综合价格与“移动成本”进行选择。移动成本采用二次函数形式，体现了消费者对产品特性或地理位置的敏感程度。研究表明：产品差异化程度越高，市场需求的价格弹性越低，企业的定价空间越大；差异化因素（如品牌、质量或兼容性）能够削弱价格竞争并推动企业转向非价格竞争。在网络经济环境下，该模型被进一步拓展，用于研究高固定成本、用户锁定效应等因素对市场垄断趋势的影响，并提出了水平差异化与垂直差异化的分析框架。

The Hotelling model, proposed by economist Harold Hotelling in 1929, is a classic framework for analyzing price stability in duopoly markets. Based on the theory of spatial competition, the model offers a correction to the market instability emphasized by the Edgeworth model, arguing that product differentiation can weaken price competition, allowing companies to establish market barriers through pricing adjustments or improved product features. The model assumes that consumer preferences are uniformly distributed along the interval [0,1], with two companies located at different locations along the line. Consumers make their choices based on a combination of price and "movement costs." The movement costs, expressed as a quadratic function, reflect consumers' sensitivity to product features or geographic location. Research has shown that the higher the degree of product differentiation, the lower the price elasticity of market demand, increasing the pricing space for companies. Differentiating factors (such as brand, quality, or compatibility) can weaken price competition and encourage companies to shift to non-price competition. In the network economy, the model has been further extended to study the impact of factors such as high fixed costs and user lock-in on market trends toward monopoly, and proposes analytical frameworks for horizontal and vertical differentiation.

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参考资料：百度、Chatgpt