# Co-Opetitive Strategy Optimization for Online Video Platforms with Multi-Homing Subscribers and Advertisers

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## Abstract

**:**

## 1. Introduction

## 2. Related Literature

#### 2.1. Two-Sided Market and Pricing Strategy

#### 2.2. Online Video Platform

#### 2.3. Co-Opetitive Strategy

## 3. Problem Formulation

#### 3.1. Single-Homing Subscriber and Advertiser

**Proposition**

**1.**

**Corollary**

**1.**

- (1)
- $\frac{\partial c{a}_{1}{}^{*s}}{\partial {c}_{2}}<0$, $\frac{\partial c{a}_{2}{}^{*s}}{\partial {c}_{1}}<0$, $\frac{\partial {n}_{S1}{}^{*s}}{\partial {c}_{2}}=-\frac{\partial {n}_{S2}{}^{*s}}{\partial {c}_{2}}<0$, $\frac{\partial {n}_{A1}{}^{*s}}{\partial {c}_{1}}>0$, $\frac{\partial {n}_{A1}{}^{*s}}{\partial {c}_{2}}<0$.
- (2)
- When${c}_{1}>{c}_{2}$, $\frac{\partial c{a}_{1}{}^{*s}}{\partial {a}_{a}}>0$, $\frac{\partial c{a}_{1}{}^{*s}}{\partial \beta}>0$, $\frac{\partial c{a}_{2}{}^{*s}}{\partial \beta}<0$, $\frac{\partial {n}_{S1}{}^{*s}}{\partial \beta}=-\frac{\partial {n}_{S2}{}^{*s}}{\partial \beta}>0$, $\frac{\partial {n}_{S1}{}^{*s}}{\partial {a}_{s}}=-\frac{\partial {n}_{S2}{}^{*s}}{\partial {a}_{s}}<0$, $\frac{\partial {n}_{A1}{}^{*s}}{\partial \beta}>0$.

#### 3.2. Multi-Homing Subscriber and Single-Homing Advertiser

**Proposition**

**2.**

**Corollary**

**2.**

- (1)
- $\frac{\partial {n}_{S12}{}^{*DS}}{\partial {a}_{s}}<0$, $\frac{\partial {n}_{S12}{}^{*DS}}{\partial \beta}>0$, $\frac{\partial {n}_{S12}{}^{*DS}}{\partial {c}_{1}}=\frac{\partial {n}_{S12}{}^{*DS}}{\partial {c}_{2}}>0$.
- (2)
- $\frac{\partial {n}_{S1}{}^{*DS}}{\partial \beta}<0$, $\frac{\partial {n}_{S1}{}^{*DS}}{\partial {c}_{1}}<0$, $\frac{\partial {n}_{S1}{}^{*DS}}{\partial {c}_{2}}<0$. When${c}_{1}>{c}_{2}$, $\frac{\partial {n}_{S1}{}^{*DS}}{\partial p{r}_{a}}>0$.

#### 3.3. Multi-Homing Subscriber and Advertiser

**Proposition**

**3.**

**Corollary**

**3.**

- (1)
- $\frac{\partial c{a}_{i}{}^{*DD}}{\partial \beta}<0$, $\frac{\partial c{a}_{i}{}^{*DD}}{\partial {c}_{-i}}<0$, $\frac{\partial c{a}_{2}{}^{*DD}}{\partial {a}_{s}}>0$.
- (2)
- $\frac{\partial {n}_{Si}{}^{*DD}}{\partial \beta}<0$, $\frac{\partial {n}_{Si}{}^{*DD}}{\partial {c}_{-i}}<0$, $\frac{\partial {n}_{S12}{}^{*DD}}{\partial \beta}>0$, $\frac{\partial {n}_{S12}{}^{*DD}}{\partial {c}_{1}}>0$, $\frac{\partial {n}_{S12}{}^{*DD}}{\partial {c}_{2}}>0$.
- (3)
- $\frac{\partial {n}_{Ai}{}^{*DD}}{\partial \beta}>0$, $\frac{\partial {n}_{A1}{}^{*DD}}{\partial {c}_{1}}>0$. $\frac{\partial {n}_{A12}{}^{*DD}}{\partial \beta}<0$, $\frac{\partial {n}_{A12}{}^{*DD}}{\partial {c}_{1}}<0$.

## 4. Comparison among Cases

**Conclusion**

**1.**

**Conclusion**

**2.**

**Conclusion**

**3.**

## 5. Numerical Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Proof of Proposition**

**1.**

**Proof of Corollary**

**1.**

**Proof of Proposition**

**2.**

**Proof of Corollary**

**2.**

**Proof of Proposition**

**3.**

**Proof of Corollary**

**3.**

**Proof**

**of**

**Conclusions.**

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Study | Two-Sided Market | Online Video Platform | Platform’s Co-Opetitive Strategy | ||
---|---|---|---|---|---|

Pricing Strategies | Multi-Homing | Video Industry | Streaming Content | ||

Fan et al. [15] | √ | - | - | - | - |

Gal-Or et al. [18] | √ | - | - | - | - |

Ambrus et al. [21] | √ | √ | √ | - | - |

Athey et al. [46] | √ | √ | - | - | - |

Li et al. [9] | √ | √ | - | - | √ |

Xie et al. [19] | √ | √ | - | - | - |

Amaldoss et al. [29] | √ | - | √ | √ | - |

Cohen and Zhang [28] | √ | √ | - | - | √ |

Our study | √ | √ | √ | √ | √ |

Decision Variables | |
---|---|

$c{a}_{i}$ | Entry fee charged by platform i for advertiser. |

Parameters | |

${\theta}_{ji}$ | Distance between platform and subscriber or advertiser, $j=s,a$. |

$v$ | Reservation utility of subscriber |

$p{r}_{j}$ | Subscriber or advertiser’s transportation cost, $j=s,a$. |

$\beta $ | Subscriber’s preference for platform’s content. |

${c}_{i}$ | Unit broadcasting rights cost of platform i for content, $i=1,2$. |

${a}_{s}$ | Negative cross-side network effect of advertiser. |

${a}_{a}$ | Positive cross-side network effect of subscriber. |

${n}_{Si}$ | Number of the subscriber on platform $i=1,2,12$. |

${n}_{Ai}$ | Number of the advertiser on platform $i=1,2,12$. |

${\pi}_{i}$ | Profit function of platform i, $i=1,2$. |

$\mathit{S}$ | $\mathit{D}\mathit{S}$ | $\mathit{D}\mathit{D}$ | |
---|---|---|---|

$c{a}_{1}$ | $pr-\frac{\left(5c-3{a}_{a}\right){a}_{s}}{3pr}$. | $pr-\frac{\left(5c-3{a}_{a}\right){a}_{s}}{3pr}$. | $\frac{{a}_{a}\left(pr-c\beta +{a}_{s}\right)-c{a}_{s}}{2pr}$. |

$c{a}_{2}$ | $pr-\frac{\left(4c-3{a}_{a}\right){a}_{s}}{3pr}$. | $pr-\frac{\left(4c-3{a}_{a}\right){a}_{s}}{3pr}$. | $\frac{{a}_{a}\left(pr-c\beta +{a}_{s}\right)}{2pr}$. |

${n}_{\mathrm{S}1}$ | $\frac{3p{r}^{3}+3pr{a}_{a}{a}_{s}-c{a}_{s}^{2}}{6\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$. | $1-\frac{c\beta}{pr}+\frac{3p{r}^{2}{a}_{s}-{a}_{s}^{2}\left(c-3{a}_{a}\right)}{6\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$. | $\frac{1}{2}-\frac{c\beta}{2pr}+\frac{2{a}_{s}p{r}^{2}-{a}_{s}^{2}\left(c-{a}_{a}\right)}{2\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$. |

${n}_{\mathrm{S}2}$ | $\frac{3p{r}^{3}+3pr{a}_{a}{a}_{s}+c{a}_{s}^{2}}{6\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$. | $1-\frac{c\beta}{pr}+\frac{3p{r}^{2}{a}_{s}+{a}_{s}^{2}\left(c+3{a}_{a}\right)}{6\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$. | $\frac{\left(pr-c\beta +{a}_{s}\right)\left(2p{r}^{2}+{a}_{a}{a}_{s}\right)}{2\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$. |

${n}_{\mathrm{S}12}$ | / | $-\frac{pr-2c\beta +{a}_{s}}{pr}$. | $\frac{c\beta \left(2p{r}^{2}+{a}_{a}{a}_{s}\right)-p{r}^{2}\left(2{a}_{s}+pr\right)}{pr\left({a}_{a}{a}_{s}+p{r}^{2}\right)}+\frac{\left(c-2{a}_{a}\right){a}_{s}^{2}}{2pr\left({a}_{a}{a}_{s}+p{r}^{2}\right)}$. |

${n}_{\mathrm{A}1}$ | $\frac{1}{2}+\frac{c{a}_{s}}{6\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. | $\frac{1}{2}+\frac{c{a}_{s}}{6\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. | $\frac{2p{r}^{2}+{a}_{a}\left(c\beta +{a}_{s}-pr\right)}{2\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. |

${n}_{\mathrm{A}2}$ | $\frac{1}{2}-\frac{c{a}_{s}}{6\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. | $\frac{1}{2}-\frac{c{a}_{s}}{6\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. | $\frac{2p{r}^{2}-c{a}_{s}+{a}_{a}\left(c\beta +{a}_{s}-pr\right)}{2\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. |

${n}_{A12}$ | / | / | $\frac{-2p{r}^{2}+2\left(pr-c\beta \right){a}_{a}+c{a}_{s}}{2\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. |

${\pi}_{1}$ | ${\pi}_{1}{}^{*s}=\frac{pr}{2}+\frac{\left(3{a}_{a}-4c\right){a}_{s}}{6pr}+\frac{{c}^{2}{a}_{s}^{2}}{18pr\left(p{r}^{2}+{a}_{a}{a}_{s}\right)},$${\pi}_{1}{}^{*DS}=\frac{p{r}^{2}+{a}_{a}{a}_{s}}{2pr}-\frac{2{a}_{s}c}{3pr}+\frac{{c}^{2}{a}_{s}^{2}}{18pr\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$, ${\pi}_{1}{}^{*DD}=\frac{{c}^{2}{a}_{s}^{2}+{a}_{a}^{2}{\left(pr-c\beta +{a}_{s}\right)}^{2}}{4\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$. | ||

${\pi}_{2}$ | ${\pi}_{2}{}^{*s}=\frac{pr-c}{2}+\frac{\left(3{a}_{a}-5c\right){a}_{s}}{6pr}+\frac{{c}^{2}{a}_{s}^{2}}{18\left(p{r}^{3}+pr{a}_{a}{a}_{s}\right)}$$,{\pi}_{2}{}^{*DS}=\frac{p{r}^{2}-2{c}^{2}\beta +{a}_{a}{a}_{s}}{2pr}-\frac{{a}_{s}c}{3pr}+\frac{{c}^{2}{a}_{s}^{2}}{18pr\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$$,{\pi}_{2}{}^{*DD}=\frac{{a}_{a}^{2}{\left(pr-c\beta +{a}_{s}\right)}^{2}}{4pr\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}-\frac{c{a}_{a}{a}_{s}\left(pr+c\beta -{a}_{s}\right)+c\left(2cp{r}^{2}\beta -2p{r}^{2}{a}_{s}+c{a}_{s}^{2}\right)}{2pr\left(p{r}^{2}+{a}_{a}{a}_{s}\right)}$. |

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**MDPI and ACS Style**

Li, J.; Gong, S.; Li, X.
Co-Opetitive Strategy Optimization for Online Video Platforms with Multi-Homing Subscribers and Advertisers. *J. Theor. Appl. Electron. Commer. Res.* **2023**, *18*, 744-764.
https://doi.org/10.3390/jtaer18010038

**AMA Style**

Li J, Gong S, Li X.
Co-Opetitive Strategy Optimization for Online Video Platforms with Multi-Homing Subscribers and Advertisers. *Journal of Theoretical and Applied Electronic Commerce Research*. 2023; 18(1):744-764.
https://doi.org/10.3390/jtaer18010038

**Chicago/Turabian Style**

Li, Jing, Shuying Gong, and Xing Li.
2023. "Co-Opetitive Strategy Optimization for Online Video Platforms with Multi-Homing Subscribers and Advertisers" *Journal of Theoretical and Applied Electronic Commerce Research* 18, no. 1: 744-764.
https://doi.org/10.3390/jtaer18010038