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

^{1}

^{2}

^{3}

^{*}

## 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.**

## References

- Netflix Shares Rise on Strong Subscriber Growth, Considers Share Buybacks. Available online: https://www.cnbc.com/2021/01/19/netflix-nflx-q4-2020-earnings.html (accessed on 19 January 2021).
- Annual Revenue of Chinese Online Video Site iQIYI in 2021. Available online: https://www.statista.com/statistics/1107850/chinese-online-video-platform-iqiyi-revenue-by-segment/ (accessed on 15 November 2022).
- TikTok. Available online: https://en.wikipedia.org/wiki/TikTok#Viral_trends (accessed on 1 March 2023).
- Armstrong, M. Competition in two-sided markets. RAND J. Econ.
**2006**, 37, 668–691. [Google Scholar] [CrossRef][Green Version] - Lu, S.; Yao, D.; Chen, X.; Grewal, R. Do Larger Audiences Generate Greater Revenues Under Pay What You Want? Evidence from a Live Streaming Platform. Mark. Sci.
**2021**, 40, 964–984. [Google Scholar] [CrossRef] - Cheng, X.; Mu, L.; Sun, Y.; Bian, Y. Optimal Pricing Decisions for the Online Video Platform Under Customer Choice. Asia-Pac. J. Oper. Res.
**2018**, 35, 1850002. [Google Scholar] [CrossRef] - World Cup Revenue Analysis and Enlightenment to Operators. Available online: https://www.sohu.com/a/241971513_488163 (accessed on 18 July 2018).
- Netflix Acquires Chinese Detective Drama Series ‘Day and Night’. Available online: https://www.hollywoodreporter.com/tv/tv-news/netflix-acquires-chinese-detective-drama-series-night-day-1062954/ (accessed on 30 November 2017).
- Li, G.; Zheng, H.; Tian, L. Information Sharing in an Online Marketplace with Co-opetitive Sellers. Prod. Oper. Manag.
**2021**, 30, 3713–3734. [Google Scholar] [CrossRef] - Rochet, J.-C.; Tirole, J. Two-sided markets: A progress report. RAND J. Econ.
**2006**, 37, 645–667. [Google Scholar] [CrossRef][Green Version] - Eisenmann, T.; Parker, G.; Van Alstyne, M.W. Strategies for two-sided markets. Harv. Bus. Rev.
**2006**, 84, 92. [Google Scholar] - Rysman, M. The Economics of Two-Sided Markets. J. Econ. Perspect.
**2009**, 23, 125–143. [Google Scholar] [CrossRef][Green Version] - Gal-Or, E.; Gal-Or, R.; Penmetsa, N. The Role of User Privacy Concerns in Shaping Competition Among Platforms. Inf. Syst. Res.
**2018**, 29, 698–722. [Google Scholar] [CrossRef] - Barros, P.P.; Kind, H.J.; Nilssen, T.; Sørgard, L. Media competition on the internet. BE J. Econ. Anal. Policy
**2005**, 4, 1–20. [Google Scholar] [CrossRef][Green Version] - Fan, M.; Kumar, S.; Whinston, A.B. Selling or Advertising: Strategies for Providing Digital Media Online. J. Manag. Inf. Syst.
**2007**, 24, 143–166. [Google Scholar] [CrossRef] - Kind, H.J.; Nilssen, T.; Sørgard, L. Business models for media firms: Does competition matter for how they raise revenue? Mark. Sci.
**2009**, 28, 1112–1128. [Google Scholar] [CrossRef][Green Version] - Reisinger, M. Platform competition for advertisers and users in media markets. Int. J. Ind. Organ.
**2012**, 30, 243–252. [Google Scholar] [CrossRef] - Gal-Or, E.; Geylani, T.; Yildirim, T.P. The Impact of Advertising on Media Bias. J. Mark. Res.
**2012**, 49, 92–99. [Google Scholar] [CrossRef] - Xie, J.; Zhu, W.; Wei, L.; Liang, L. Platform competition with partial multi-homing: When both same-side and cross-side network effects exist. Int. J. Prod. Econ.
**2021**, 233, 108016. [Google Scholar] [CrossRef] - Choi, J.P. Tying in two-sided markets with multi-homing. J. Ind. Econ.
**2010**, 58, 607–626. [Google Scholar] [CrossRef][Green Version] - Ambrus, A.; Calvano, E.; Reisinger, M. Either or Both Competition: A “Two-Sided” Theory of Advertising with Overlapping Viewerships. Am. Econ. J. Microecon.
**2016**, 8, 189–222. [Google Scholar] [CrossRef][Green Version] - Anderson, S.P.; Foros, Ø.; Kind, H.J. The importance of consumer multihoming (joint purchases) for market performance: Mergers and entry in media markets. J. Econ. Manag. Strategy
**2019**, 28, 125–137. [Google Scholar] [CrossRef][Green Version] - D’Annunzio, A.; Russo, A. Ad Networks and Consumer Tracking. Manag. Sci.
**2020**, 66, 5040–5058. [Google Scholar] [CrossRef][Green Version] - Gallaugher, J.M.; Wang, Y.-M. Understanding Network Effects in Software Markets: Evidence from Web Server Pricing. MIS Q.
**2002**, 26, 303. [Google Scholar] [CrossRef][Green Version] - Rysman, M. Competition Between Networks: A Study of the Market for Yellow Pages. Rev. Econ. Stud.
**2004**, 71, 483–512. [Google Scholar] [CrossRef] - Rysman, M. An empirical analysis of payment card usage. J. Ind. Econ.
**2007**, 55, 1–36. [Google Scholar] [CrossRef] - Lee, R.S. Vertical Integration and Exclusivity in Platform and Two-Sided Markets. Am. Econ. Rev.
**2013**, 103, 2960–3000. [Google Scholar] [CrossRef][Green Version] - Cohen, M.C.; Zhang, R. Competition and coopetition for two-sided platforms. Prod. Oper. Manag.
**2022**, 31, 1997–2014. [Google Scholar] [CrossRef] - Amaldoss, W.; Du, J.; Shin, W. Media Platforms’ Content Provision Strategies and Sources of Profits. Mark. Sci.
**2022**, 40, 527–547. [Google Scholar] [CrossRef] - Anderson, S.; Coate, S. Market Provision of Broadcasting: A Welfare Analysis. Rev. Econ. Stud.
**2005**, 72, 947–972. [Google Scholar] [CrossRef] - Wilbur, K.C. A Two-Sided, Empirical Model of Television Advertising and Viewing Markets. Mark. Sci.
**2008**, 27, 356–378. [Google Scholar] [CrossRef][Green Version] - Lin, Y.; Yao, D.; Chen, X. Happiness Begets Money: Emotion and Engagement in Live Streaming. J. Mark. Res.
**2021**, 58, 417–438. [Google Scholar] [CrossRef] - Shriver, S.K.; Nair, H.S.; Hofstetter, R. Social Ties and User-Generated Content: Evidence from an Online Social Network. Manag. Sci.
**2013**, 59, 1425–1443. [Google Scholar] [CrossRef][Green Version] - Brandenburger, A.M.; Nalebuff, B.J. Universal lessons every manager can learn from Andy Grove’s paranoia. Harv. Bus. Rev.
**1996**, 169, 168–175. [Google Scholar] - Brandenburger, A.M.; Nalebuff, B.J. Co-Opetition; Currency Doubleday: New York, NY, USA, 2011. [Google Scholar]
- Brandenburger, A.M.; Nalebuff, B.J. The rules of co-opetition. Harv. Bus. Rev.
**2021**, 48–57. [Google Scholar] - Casadesus-Masanell, R.; Yoffie, D.B. Wintel: Cooperation and Conflict. Manag. Sci.
**2007**, 53, 584–598. [Google Scholar] [CrossRef] - Wright, C.P.; Groenevelt, H.; Shumsky, R.A. Dynamic Revenue Management in Airline Alliances. Transp. Sci.
**2010**, 44, 15–37. [Google Scholar] [CrossRef] - Niu, B.; Chen, K.; Fang, X.; Yue, X.; Wang, X. Technology Specifications and Production Timing in a Co-Opetitive Supply Chain. Prod. Oper. Manag.
**2019**, 28, 1990–2007. [Google Scholar] [CrossRef] - Jung, S.H.; Kouvelis, P. On Co-opetitive Supply Partnerships with End-Product Rivals: Information Asymmetry, Dual Sourcing and Supply Market Efficiency. Manuf. Serv. Oper. Manag.
**2022**, 24, 1040–1055. [Google Scholar] [CrossRef] - Shi, S.; Wang, C.; Cheng, T.C.E.; Liu, S. Manufacturer encroachment with an e-commerce division. Prod. Oper. Manag. 2023. [CrossRef]
- Ozcan, P.; Santos, F.M. The market that never was: Turf wars and failed alliances in mobile payments. Strateg. Manag. J.
**2015**, 36, 1486–1512. [Google Scholar] [CrossRef] - Wu, H.; Zheng, H.; Li, J. The interplay between quality improvement and information acquisition in an E-commerce supply chain. Ann. Oper. Res.
**2021**, 1–24. [Google Scholar] [CrossRef] - Zhong, Q.; Wang, J.; Zou, Z.; Lai, X. The incentives for information sharing in online retail platforms. Transp. Res. Part E Logist. Transp. Rev.
**2023**, 172, 103050. [Google Scholar] [CrossRef] - Wang, P.; Du, S.; Hu, L.; Tang, W. Logistics choices in a platform supply chain: A co-opetitive perspective. J. Oper. Res. Soc.
**2022**, 74, 93–111. [Google Scholar] [CrossRef] - Athey, S.; Calvano, E.; Gans, J.S. The Impact of Consumer Multi-homing on Advertising Markets and Media Competition. Manag. Sci.
**2018**, 64, 1574–1590. [Google Scholar] [CrossRef][Green Version]

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)}$. |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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