《考虑市场结构差异的SaaS定价博弈研究》定价策略对比研究（2）

摘要：This post will introduce the comparative study of pricing strategies in the SaaS monopoly market from the intensive reading master

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“喆学（126）：精读硕士论文

《考虑市场结构差异的SaaS定价博弈研究》

SaaS 垄断市场下定价策略对比研究（2）”

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"Zhexue (126): Intensive reading of master's thesis

"A study on SaaS pricing game considering market structure differences"

Comparative Study on Pricing Strategies in SaaS Monopoly Market (2)"

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本期推文将从思维导图、精读内容、知识补充三个方面介绍精读硕士论文《考虑市场结构差异的SaaS定价博弈研究》的SaaS 垄断市场下定价策略对比研究。

This post will introduce the comparative study of pricing strategies in the SaaS monopoly market from the intensive reading master's thesis "Research on SaaS Pricing Game Considering Market Structure Differences" from three aspects: mind mapping, intensive reading content, and knowledge supplement.

一、思维导图（Mind Maps）

二、精读内容（Intensive reading content）

(1)模型构建(Model building)

1.固定定价(Fixed Pricing)

文章讨论了SaaS提供商在固定定价机制下的定价策略。定义了用户剩余，并分析了用户购买行为。SaaS提供商的利润最大化问题被表述为最大化利润函数。结论指出，最优价格为2γ^2，利润为2γ^3/[e^2δ(1+γ/δ)δ/γ+1]，随γ增加而增加，随δ减小而减小。公式(3.8)给出了最优价格的计算方法。

This article discusses the pricing strategy of SaaS providers under a fixed pricing mechanism. User surplus is defined and user purchasing behavior is analyzed. The profit maximization problem of SaaS providers is expressed as maximizing the profit function. The conclusion shows that the optimal price is 2γ^2 and the profit is 2γ^3/[e^2δ(1+γ/δ)δ/γ+1], which increases with γ and decreases with δ. Formula (3.8) gives the calculation method of the optimal price.

通过数学推导，得出了SaaS提供商的最优价格和利润公式。研究表明，随着用户偏好度的增加，SaaS提供商的利润也会增加，而随着平均风险度的增加，利润会减少。SaaS提供商在定价时需要考虑风险和用户偏好这两个因素，以制定合适的价格策略。此外，用户的消费行为也会受到这两个因素的影响。

Through mathematical derivation, the optimal price and profit formula of SaaS providers is obtained. Studies have shown that as user preference increases, the profit of SaaS providers will also increase, while as the average risk increases, the profit will decrease. SaaS providers need to consider the two factors of risk and user preference when setting prices in order to formulate appropriate pricing strategies. In addition, user consumption behavior will also be affected by these two factors.

2.按用量定价(Usage-based pricing)

文章首先介绍了用量定价机制下的价格设计，强调了两个约束条件：消费者效用和收入非负。接着，假设用户剩余，并分析了用户购买行为。当用户不购买服务时，满足特定条件。SaaS提供商的利润最大化问题被表述为最大化利润函数。结论指出，在用量定价机制下，SaaS提供商的最优价格表单由特定公式给出。

The article first introduces the price design under the usage pricing mechanism, emphasizing two constraints: consumer utility and non-negative income. Then, it assumes user surplus and analyzes user purchasing behavior. When the user does not purchase the service, a specific condition is met. The profit maximization problem of the SaaS provider is expressed as maximizing the profit function. The conclusion points out that under the usage pricing mechanism, the optimal price list of the SaaS provider is given by a specific formula.

图片内容讨论了SaaS提供商在准确评估服务风险时的定价策略。结论指出，当风险已知时，SaaS提供商可以制定最优价格表单，并计算出相应的利润。利润会随着风险评估的准确性而增加。此外，SaaS提供商可以根据不同的用户风险等级制定相应的定价策略，从而更好地满足不同细分市场的需求，加快SaaS服务在各市场的推广和应用。

The picture content discusses the pricing strategy of SaaS providers when accurately assessing service risks. The conclusion points out that when the risks are known, SaaS providers can formulate the best price list and calculate the corresponding profits. The profits will increase with the accuracy of risk assessment. In addition, SaaS providers can formulate corresponding pricing strategies according to different user risk levels, so as to better meet the needs of different market segments and accelerate the promotion and application of SaaS services in various markets.

3.混合定价(Hybrid pricing)

混合定价机制结合了固定定价和按用量定价两种方式。用户根据剩余价值选择购买方式。SaaS提供商需要确定最优价格和策略，以最大化综合利润。通过分析用户行为和市场覆盖范围，提供商可以制定出适合不同市场特征的定价策略。

The hybrid pricing mechanism combines fixed pricing and usage-based pricing. Users choose the purchase method based on the residual value. SaaS providers need to determine the optimal price and strategy to maximize the overall profit. By analyzing user behavior and market coverage, providers can develop pricing strategies that are suitable for different market characteristics.

在混合定价机制下，SaaS提供商如何根据风险评估和用户特征来制定最优定价策略。结论指出，当风险一定时，SaaS提供商可以设定最优的用量定价和固定定价，以最大化利润。为了保证两种定价机制都有用户选择，需要满足特定条件。用户会根据自身价值选择最合适的定价机制。混合定价机制有助于吸引更多用户，扩大市场。SaaS提供商可以根据用户特征将用户分为不同群体，制定相应的定价策略，从而提高利润。

Under the hybrid pricing mechanism, how can SaaS providers develop the optimal pricing strategy based on risk assessment and user characteristics. The conclusion points out that when the risk is certain, SaaS providers can set the optimal usage pricing and fixed pricing to maximize profits. In order to ensure that both pricing mechanisms have user choices, specific conditions need to be met. Users will choose the most appropriate pricing mechanism based on their own value. The hybrid pricing mechanism helps to attract more users and expand the market. SaaS providers can divide users into different groups according to user characteristics and develop corresponding pricing strategies to increase profits.

(2)模型结果分析(Model results analysis)

1.采纳时机分析(Adoption timing analysis)

文章分析了三种定价机制的优缺点，并通过比较它们的利润，得出结论：当市场上高价值用户较少时，SaaS提供商应采用单一固定定价机制；而当高价值用户较多时，应采用混合定价机制。这种策略选择有助于SaaS提供商根据不同市场特征获得最大利润。

The article analyzes the advantages and disadvantages of three pricing mechanisms, and by comparing their profits, it is concluded that when there are fewer high-value users in the market, SaaS providers should adopt a single fixed pricing mechanism; when there are more high-value users, a mixed pricing mechanism should be adopted. This strategic choice helps SaaS providers obtain maximum profits based on different market characteristics.

结论指出，当市场平均用户偏好度较低时，固定定价机制是最佳选择，因为此时市场上高价值用户较少，而大多数用户为低价值用户。固定定价机制可以保证SaaS提供商在市场初期获得稳定利润，并吸引更多用户。当市场平均用户偏好度较高时，混合定价机制是最佳选择，因为它能扩大用户群体并提高利润。此外，SaaS提供商还可以通过识别用户风险来制定最佳定价策略。图3.1展示了某个函数随时间的变化趋势。

The conclusion points out that when the average user preference in the market is low, the fixed pricing mechanism is the best choice, because at this time there are fewer high-value users in the market, and most users are low-value users. The fixed pricing mechanism can ensure that SaaS providers obtain stable profits in the early stage of the market and attract more users. When the average user preference in the market is high, the mixed pricing mechanism is the best choice because it can expand the user base and increase profits. In addition, SaaS providers can also formulate the best pricing strategy by identifying user risks. Figure 3.1 shows the trend of a function over time.

2.用户消费行为分析(Analysis of user consumption behavior)

文章内容分析了用户在不同风险环境下的消费行为，特别是在用量定价和固定定价机制下的选择。文章指出，用户剩余随用户偏好和风险的变化而变化，影响用户选择哪种定价机制。在高风险环境下，用户倾向于选择固定定价机制；在低风险环境下，用户可能更倾向于用量定价机制。文章还讨论了用户从用量定价转向固定定价的最低阈值，以及在不同风险环境下，SaaS提供商如何通过调整定价策略来吸引用户。

The article analyzes the consumption behavior of users under different risk environments, especially the choices under usage pricing and fixed pricing mechanisms. The article points out that user surplus changes with user preferences and risks, affecting which pricing mechanism users choose. In a high-risk environment, users tend to choose a fixed pricing mechanism; in a low-risk environment, users may prefer a usage pricing mechanism. The article also discusses the minimum threshold for users to switch from usage pricing to fixed pricing, and how SaaS providers can attract users by adjusting pricing strategies under different risk environments.

接着讨论了在混合定价机制下，用户选择定价机制的条件。结论指出，在高风险环境下，只有高偏好用户会从按用量定价转向固定定价机制。这是因为高风险降低了用户的效用，只有高偏好用户在高风险下仍能从SaaS服务中获得足够的价值。固定定价机制独立于使用情况，用户承担的风险较小。结论还指出，用户选择将受偏好和风险因素的影响，遵循特定条件。

Then the conditions for users to choose pricing mechanisms under a mixed pricing mechanism are discussed. The conclusion points out that in a high-risk environment, only high-preference users will switch from usage-based pricing to a fixed pricing mechanism. This is because high risk reduces the user's utility, and only high-preference users can still get enough value from SaaS services under high risk. The fixed pricing mechanism is independent of usage, and users bear less risk. The conclusion also points out that user choices will be affected by preference and risk factors and follow specific conditions.

推论3.1指出，在高风险环境下，不购买SaaS服务的用户数量增加，且用户更倾向于按用量定价机制。随着SaaS服务风险的升高，市场规模逐渐缩小，部分用户会从固定定价转向按用量定价。图3.2展示了混合定价下风险对用户选择的影响，说明了用户在不同风险环境下的购买偏好变化。

Corollary 3.1 points out that in a high-risk environment, the number of users who do not purchase SaaS services increases, and users are more inclined to a usage-based pricing mechanism. As the risk of SaaS services increases, the market size gradually shrinks, and some users will switch from fixed pricing to usage-based pricing. Figure 3.2 shows the impact of risk on user choices under mixed pricing, illustrating the changes in user purchasing preferences under different risk environments.

3.社会福利效应分析(Analysis of social welfare effect)

首先定义了社会福利为提供商利润和用户剩余之和。在固定定价机制下，通过公式计算了用户剩余和社会福利。接着，在混合定价机制下，用户剩余由两部分组成，分别对应固定定价和按用量定价的用户。通过比较不同定价机制下的社会福利，得出混合定价机制下的社会福利大于单一按用量定价机制。进一步比较混合定价和固定定价机制下的社会福利，得出混合定价机制下的社会福利更大。

First, social welfare is defined as the sum of provider profit and user surplus. Under the fixed pricing mechanism, user surplus and social welfare are calculated by formula. Then, under the mixed pricing mechanism, user surplus consists of two parts, corresponding to fixed pricing and usage-based pricing users. By comparing the social welfare under different pricing mechanisms, it is concluded that the social welfare under the mixed pricing mechanism is greater than that under the single usage-based pricing mechanism. Further comparison of the social welfare under the mixed pricing and fixed pricing mechanisms shows that the social welfare under the mixed pricing mechanism is greater.

通过图3.3，指出当参数γ远大于c时，混合定价机制的社会福利大于单一固定定价机制。这说明了单位交易成本的高低是按用量定价机制能否创造价值的关键因素。图中函数在初期下降后逐渐上升，最终趋于稳定。

Figure 3.3 shows that when the parameter γ is much greater than c, the social welfare of the mixed pricing mechanism is greater than that of the single fixed pricing mechanism. This shows that the level of unit transaction cost is a key factor in whether the usage-based pricing mechanism can create value. The function in the figure gradually rises after an initial decline and eventually stabilizes.

三、知识补充（Knowledge supplement）

社会福利效应是指某一事件、政策或行为对社会整体福利的影响。社会福利通常包括经济增长、收入分配、就业、教育、健康、环境质量等方面。社会福利效应可以是正面的，也可以是负面的，具体取决于相关因素如何相互作用。

Social welfare effects refer to the impact of an event, policy or behavior on the overall welfare of society. Social welfare usually includes economic growth, income distribution, employment, education, health, environmental quality and other aspects. Social welfare effects can be positive or negative, depending on how the relevant factors interact.

正面效应：

Positive effects:

1.经济增长：通过提高生产力和就业机会，增加社会财富，改善人民生活水平。

1. Economic growth: increase social wealth and improve people's living standards by improving productivity and employment opportunities.

2.收入分配：通过税收和转移支付等手段，减少贫富差距，提高社会公平性。

2. Income distribution: reduce the gap between the rich and the poor and improve social fairness through means such as taxation and transfer payments.

3.教育和健康：提高教育和医疗服务的可及性和质量，增强人力资本，促进社会稳定和发展。

3. Education and health: improve the accessibility and quality of education and medical services, enhance human capital, and promote social stability and development.

4.环境保护：通过可持续发展政策，保护自然资源和环境，提高生活质量。

4. Environmental protection: protect natural resources and the environment through sustainable development policies and improve the quality of life.

负面效应：

Negative effects:

1.资源分配不均：可能导致某些群体受益过多，而其他群体受益不足，加剧社会不平等。

1. Uneven distribution of resources: may cause some groups to benefit too much while other groups benefit insufficiently, exacerbating social inequality.

2.经济波动：某些政策可能引发经济不稳定，如通货膨胀或失业增加。

2. Economic fluctuations: certain policies may trigger economic instability, such as inflation or increased unemployment.

3.环境破坏：过度开发和污染可能损害环境，影响后代的福利。

3. Environmental damage: overexploitation and pollution may damage the environment and affect the welfare of future generations.

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