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Research on Pricing Strategies of Video Platform and Advertiser Considering Consumers’ Advertising Aversion

Abstract: This paper establishes a pricing game model between a video platform and an advertiser with consideration of consumers’ aversion to advertisements. By solving the optimal video fee of the platform and the advertiser’s advertisement price, we analyze the impacts of key factors such as consumers’ advertising aversion, advertising time-length and platform service level on the strategies of both parties of the game. Findings show that as consumers’ advertising aversion or advertising time-length increases, the platform increases the video fee, and the advertiser increases the advertising price. The advertiser prices lower when the service difference received by paid users and free users of the platform is large; however, the platform lowers the video fee when such difference shrinks. Our findings contribute to provide some management insights for the online video platform and the advertiser in setting pricing strategies.

1. 引言

2. 文献综述

3. 模型描述

Table 1. Related parameters of the model

3.1. 消费者效用

${u}_{p}=v-p,$ (1)

${u}_{f}=\theta v-\gamma a,$ (2)

${v}_{0}=\frac{\gamma a}{\theta },\text{\hspace{0.17em}}{v}_{1}=\frac{\gamma a-p}{\theta -1}.$ (3)

Figure 1. Consumer demand

${D}_{1}=\frac{p+\theta -\gamma a-1}{\theta -1},$ (4)

${D}_{2}=\frac{\gamma a-p\theta }{\left(\theta -1\right)\theta }.$ (5)

3.2. 平台与广告商的利润函数

${\pi }_{l}={D}_{1}p+{D}_{2}b,$ (6)

${\pi }_{s}={D}_{2}\left(c-b\right)-\eta a,$ (7)

3.3. 平台与广告商的最优策略

${\pi }_{l}=\frac{p{\theta }^{2}-p\left(\gamma a+b-p+1\right)\theta +\gamma ab}{\left(\theta -1\right)\theta },$ (8)

$p=\frac{1+\gamma a+b-\theta }{2},$ (9)

${b}^{*}=\frac{{\theta }^{\text{2}}+\left(-\gamma a+c-\text{1}\right)\theta +\text{2}\gamma a}{\text{2}\theta },$ (10)

${p}^{*}=\frac{-{\theta }^{2}+\left(\gamma a+c+1\right)\theta +2\gamma a}{4\theta }.$ (11)

$\begin{array}{l}{\pi }_{s}^{\ast }=\frac{1}{8{\theta }^{2}\left(\theta -1\right)}\left[-{\theta }^{4}+\left(\left(2\gamma -8\eta \right)a+2c+2\right){\theta }^{3}+\left(8\eta -{\gamma }^{2}{a}^{2}-\left(2c+6\right)\gamma a-{\left(c+1\right)}^{2}\right){\theta }^{2}\\ \text{}\text{}+4\gamma a\left(\gamma a+c+1\right)\theta -4{\gamma }^{2}{a}^{2}\right]\end{array}$ (12)

$\begin{array}{l}{\pi }_{1}^{\ast }=\frac{1}{16{\theta }^{2}\left(\theta -1\right)}\left[-{\theta }^{4}+\left(2\gamma a+2c+2\right){\theta }^{3}+\left(-{\gamma }^{2}{a}^{2}-2a\left(c-5\right)\gamma -{\left(c+1\right)}^{2}\right){\theta }^{2}\\ \text{}-4\gamma a\left(3\gamma a-c+3\right)\theta +12{\gamma }^{2}{a}^{2}\right]\end{array}$ (13)

4. 管理分析

4.1. 决策分析

4.2. 利润分析

$\frac{\text{d}{\pi }_{1}^{*}}{\text{d}a}=\frac{\gamma \left(-{\theta }^{\text{3}}+\left(\gamma a+c-\text{5}\right){\theta }^{\text{2}}+\left(\text{12}\gamma a-2c+\text{6}\right)\theta -\text{12}\gamma a\right)}{\text{8}{\theta }^{\text{2}}\left(1-\theta \right)}$

$0<\theta \le 4\sqrt{3}-6$ 时，原函数在 $a<\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{\gamma \left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递增，在 $a>\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{\gamma \left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递减；当 $4\sqrt{3}-6<\theta <1$ 时，原函数在 $a<\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{\gamma \left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递减，在 $a>\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{\gamma \left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递增。

1) 当效用折扣系数较小( $0<\theta \le 4\sqrt{3}-6$ )时，平台的最优收益 ${\pi }_{l}^{*}$ 随消费者广告厌恶水平 $\gamma$ 先增加后减少；反之，当效用折扣系数较大( $4\sqrt{3}-6<\theta <1$ )时，平台的最优收益 ${\pi }_{l}^{*}$ 随消费者广告厌恶水平 $\gamma$ 先减少后增加。

2) 广告商的最优利润 ${\pi }_{s}^{*}$ 随消费者广告厌恶水平 $\gamma$ 的增加而减少。

$\frac{\text{d}{\pi }_{l}^{*}}{\text{d}\gamma }=\frac{a\left(-{\theta }^{\text{3}}+\left(\gamma a+c-\text{5}\right){\theta }^{\text{2}}+\left(\text{12}\gamma a-2c+\text{6}\right)\theta -\text{12}\gamma a\right)}{\text{8}{\theta }^{\text{2}}\left(1-\theta \right)}$

$0<\theta \le 4\sqrt{3}-6$ 时，原函数在 $\gamma <\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{a\left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递增，在 $\gamma >\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{a\left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递减；当 $4\sqrt{3}-6<\theta <1$ 时，原函数在 $\gamma <\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{a\left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递减，在 $\gamma >\frac{\theta \left({\theta }^{2}-c\theta +5\theta +2c-6\right)}{a\left({\theta }^{2}+12\theta -12\right)}$ 范围内单调递增。

2) 对广告商最优利润 ${\pi }_{s}^{*}$ 关于消费者广告厌恶水平 $\gamma$ 求导，得到

$\frac{\text{d}{\pi }_{s}^{*}}{\text{d}\gamma }=\frac{a\left(\theta -\text{2}\right)\left(-{\theta }^{\text{2}}+\left(\gamma a+c+\text{1}\right)\theta -\text{2}\gamma a\right)}{\text{4}{\theta }^{\text{2}}\left(1-\theta \right)}$

4.3. 数值分析

Figure 2. Effects of discount factor on profits of platform and advertiser

5. 结语

1) 消费者对贴片广告厌恶增加反而促使广告商提高广告投放定价，因而导致广告商的利润逐渐变少；平台则会提高视频收费定价，并且在免费用户和付费用户服务水平差距较大时，平台最优收益呈先增大后减小的趋势，反之呈先减小后增大的趋势。

2) 广告商在免费用户效用折扣系数较小时，选择降低广告投放定价；在效用折扣系数较大时，提高广告投放价格，在不同情形下合理出价让广告商的最优利润逐渐增加。平台的视频收费定价随效用折扣系数的增加而降低，而平台收益随效用折扣系数的增加呈先减少后增加的趋势。

3) 广告商广告投放定价以及平台的视频收费定价会随着广告时长的增加而提高；当免费用户和付费用户服务水平差距较大时，平台最优收益先增大后减小，在差距较小时先减小后增大。

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