# Content Quality Assurance on Media Platforms with User-Generated Content

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*J. Theor. Appl. Electron. Commer. Res.*

**2023**,

*18*(3), 1660-1686; https://doi.org/10.3390/jtaer18030084

## Abstract

**:**

## 1. Introduction

## 2. Additional Literature

#### 2.1. Media Platform Operational Strategies

#### 2.2. Impact of User Participation Decisions in Platform Competition

#### 2.3. Platform Performance Investments

## 3. Model Setup

## 4. Equilibrium Analysis

- Consumers and content producers are both single-homing (S-S scenario).
- Consumers are multi-homing, and producers are single-homing (M-S scenario).
- Consumers are single-homing, and producers are multi-homing (S-M scenario).
- Consumers and content producers are both multi-homing (M-M scenario).

#### 4.1. Single-Homing on Both Sides

**Proposition**

**1.**

- (i)
- The equilibrium exists and is unique if the consumers’ disutility from advertising is sufficiently large with $\beta >{\beta}_{1}^{{}^{\prime}}$.
- (ii)
- In equilibrium, the level of advertising on platform i is given by$${a}^{i,SS}=\frac{{t}_{c}{t}_{p}-{n}_{c}{n}_{p}}{\beta {t}_{p}}$$and the level of CQA investment on platform i is$${\delta}^{i,SS}=\frac{r\left(\gamma {t}_{p}-{n}_{c}\right)}{2c\beta {t}_{p}}.$$
- (iii)
- In equilibrium, the number of consumers and producers on platform i is$${Q}_{c}^{i,SS}=\frac{1}{2}and{Q}_{p}^{i,SS}=\frac{1}{2}.$$

**Proof.**

**Corollary**

**1.**

- (i)
- As the cross-network effects ${n}_{c}$ obtained by consumers increase, both the CQA investment and the level of advertising decrease, i.e.,$$\frac{\partial {\delta}^{i,SS}}{\partial {n}_{c}}<0and\frac{\partial {a}^{i,SS}}{\partial {n}_{c}}0.$$
- (ii)
- As the cross-network effects ${n}_{p}$ obtained by producers increase, the CQA investment is not affected, but the level of advertising decreases, i.e.,$$\frac{\partial {\delta}^{i,SS}}{\partial {n}_{p}}=0and\frac{\partial {a}^{i,SS}}{\partial {n}_{p}}0.$$
- (iii)
- As consumers’ sensitivity γ to CQA investment increases, the CQA investment increases, but the level of advertising is not affected, i.e.,$$\frac{\partial {\delta}^{i,SS}}{\partial \gamma}>0and\frac{\partial {a}^{i,SS}}{\partial \gamma}=0.$$

**Proof.**

#### 4.2. Multi-Homing Consumers and Single-Homing Producers

**Proposition**

**2.**

- (i)
- The equilibrium exists and is unique if the consumers’ disutility from advertising is sufficiently large with $\beta >{\beta}_{2}^{{}^{\prime}}$.
- (ii)
- In equilibrium, the level of advertising on platform i is given by$${a}^{i,MS}=\frac{c{t}_{c}{n}_{c}\left({t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)}{c\beta {t}_{c}\left(4{t}_{c}{t}_{p}-3{n}_{c}{n}_{p}\right)-r\gamma \left({t}_{c}\left(2\gamma {t}_{p}-{n}_{c}\right)-\gamma {n}_{c}{n}_{p}\right)}$$and the CQA investment on platform i is$${\delta}^{i,MS}=\frac{r{n}_{c}\left(\gamma \left(2{t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)-{t}_{c}{n}_{c}\right)}{2c\beta {t}_{c}\left(4{t}_{c}{t}_{p}-3{n}_{c}{n}_{p}\right)-2r\gamma \left({t}_{c}\left(2\gamma {t}_{p}-{n}_{c}\right)-\gamma {n}_{c}{n}_{p}\right)}.$$
- (iii)
- In equilibrium, the number of consumers on platform i is$${Q}_{c}^{i,MS}=\frac{c\beta {n}_{c}\left(2{t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)}{2c\beta {t}_{c}\left(4{t}_{c}{t}_{p}-3{n}_{c}{n}_{p}\right)-2r\gamma \left({t}_{c}\left(2\gamma {t}_{p}-{n}_{c}\right)-\gamma {n}_{c}{n}_{p}\right)}$$and the number of producers on platform i is$${Q}_{p}^{i,MS}=\frac{1}{2}.$$

**Proof.**

**Corollary**

**2.**

- (i)
- The cross-network effects ${n}_{c}$ obtained by consumers have an ambiguous effect on both the CQA investment and the level of advertising, i.e.,$$\begin{array}{ccc}\hfill \frac{\partial {\delta}^{i,MS}}{\partial {n}_{c}}& >& 0\iff r<{r}_{MS,1}^{\prime}and\gamma {\gamma}_{MS,1}^{\prime},\hfill \\ \hfill \frac{\partial {a}^{i,MS}}{\partial {n}_{c}}& & 0\iff r{r}_{MS,2}^{\prime}and\gamma {\gamma}_{MS,2}^{\prime}.\hfill \end{array}$$
- (ii)
- The cross-network effects ${n}_{p}$ obtained by producers have an ambiguous effect on both the CQA investment and the level of advertising, i.e.,$$\begin{array}{ccc}\hfill \frac{\partial {\delta}^{i,MS}}{\partial {n}_{p}}& >& 0\iff \gamma >{\gamma}_{MS,3}^{\prime},\hfill \\ \hfill \frac{\partial {a}^{i,MS}}{\partial {n}_{p}}& >& 0\iff r>{r}_{MS,4}^{\prime}and\gamma {\gamma}_{MS,4}^{\prime}.\hfill \end{array}$$
- (iii)
- As consumers’ sensitivity γ to CQA investment increases, both the CQA investment and the level of advertising increase, i.e.,$$\frac{\partial {\delta}^{i,MS}}{\partial \gamma}>0and\frac{\partial {a}^{i,MS}}{\partial \gamma}0.$$

**Proof.**

#### 4.3. Single-Homing Consumers and Multi-Homing Producers

**Proposition**

**3.**

- (i)
- The equilibrium exists and is unique if the consumers’ disutility from advertising is sufficiently large with $\beta >{\beta}_{1}^{{}^{\prime}}$.
- (ii)
- In equilibrium, the level of advertising on platform i is given by$${a}^{i,SM}=\frac{{t}_{c}{t}_{p}-{n}_{c}{n}_{p}}{\beta {t}_{p}}$$and the CQA investment on platform i is$${\delta}^{i,SM}=\frac{r\left(\gamma {t}_{p}-{n}_{c}\right)}{2c\beta {t}_{p}}.$$
- (iii)
- In equilibrium, the number of consumers on platform i is$${Q}_{c}^{i,SM}=\frac{1}{2}$$and the number of producers on platform i is$${Q}_{p}^{i,SM}=\frac{r{n}_{c}+{t}_{p}\left(c\beta {n}_{p}-r\gamma \right)}{2c\beta {t}_{p}^{2}}.$$

**Proof.**

**Corollary**

**3.**

- (i)
- As the cross-network effects ${n}_{c}$ obtained by consumers increase, both the CQA investment and the level of advertising decrease, i.e.,$$\frac{\partial {\delta}^{i,SM}}{\partial {n}_{c}}<0and\frac{\partial {a}^{i,SM}}{\partial {n}_{c}}0.$$
- (ii)
- As the cross-network effects ${n}_{p}$ obtained by producers increase, the CQA investment is unaffected, but the level of advertising decreases, i.e.,$$\frac{\partial {\delta}^{i,SM}}{\partial {n}_{p}}=0and\frac{\partial {a}^{i,SM}}{\partial {n}_{p}}0.$$
- (iii)
- As consumers’ sensitivity γ to CQA investment increases, the CQA investment increases, but the level of advertising is unaffected, i.e.,$$\frac{\partial {\delta}^{i,SM}}{\partial \gamma}>0and\frac{\partial {a}^{i,SM}}{\partial \gamma}=0.$$

**Proof.**

#### 4.4. Multi-Homing on Both Sides

**Proposition**

**4.**

- (i)
- The equilibrium exists and is unique if the consumers’ disutility from advertising is sufficiently large with $\beta >{\beta}_{3}^{{}^{\prime}}$.
- (ii)
- In equilibrium, the level of advertising on platform i is given by$${a}^{i,MM}=\frac{c{n}_{c}\left({n}_{p}-{t}_{p}\right)\left({t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)}{{t}_{p}\left(r\gamma \left(\gamma {t}_{p}+{n}_{c}\right)-2c\beta \left({t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)\right)}$$and the level of CQA investment on platform i is$${\delta}^{i,MM}=\frac{r\gamma {n}_{c}\left({n}_{p}-{t}_{p}\right)}{r\gamma \left(\gamma {t}_{p}+{n}_{c}\right)-2c\beta \left({t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)}.$$
- (iii)
- In equilibrium, the number of consumers on platform i is$${Q}_{c}^{i,MM}=\frac{c\beta {n}_{c}\left({n}_{p}-{t}_{p}\right)}{r\gamma \left(\gamma {t}_{p}+{n}_{c}\right)-2c\beta \left({t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)}$$and the number of producers on platform i is$${Q}_{p}^{i,MM}=\frac{r\gamma {t}_{p}\left({n}_{c}+\gamma {n}_{p}\right)-c\beta {n}_{p}\left(2{t}_{c}{t}_{p}-{n}_{c}\left({t}_{p}+{n}_{p}\right)\right)}{{t}_{p}\left(r\gamma \left(\gamma {t}_{p}+{n}_{c}\right)-2c\beta \left({t}_{c}{t}_{p}-{n}_{c}{n}_{p}\right)\right)}.$$

**Proof.**

**Corollary**

**4.**

- (i)
- As the cross-network effects ${n}_{c}$ obtained by consumers increase, both the CQA investment and the level of advertising level decrease, i.e.,$$\frac{\partial {\delta}^{i,MM}}{\partial {n}_{c}}<0and\frac{\partial {a}^{i,MM}}{\partial {n}_{c}}0.$$
- (ii)
- The cross-network effects ${n}_{p}$ obtained by producers have an ambiguous effect on both the CQA investment and the level of advertising, i.e.,$$\begin{array}{ccc}\hfill \frac{\partial {\delta}^{i,MM}}{\partial {n}_{p}}& >& 0\iff r>{r}_{MM,1}^{\prime},\hfill \\ \hfill \frac{\partial {a}^{i,MM}}{\partial {n}_{p}}& >& 0\iff r>{r}_{MM,2}^{\prime}and{n}_{c}{n}_{MM,1}^{\prime}.\hfill \end{array}$$
- (iii)
- As consumers’ sensitivity γ to CQA investment increases, both the CQA investment and the level of advertising decrease, i.e.,$$\frac{\partial {\delta}^{i,MM}}{\partial \gamma}<0and\frac{\partial {a}^{i,MM}}{\partial \gamma}0.$$

**Proof.**

#### 4.5. Comparison

**Proposition**

**5.**

- (i)
- Consumers are multi-homing and producers are single-homing (M-S scenario) if the network effects obtained by producers are sufficiently weak, i.e.,$${n}_{p}<\frac{{t}_{c}\left(2{t}_{p}\left(c\beta \left(2{t}_{c}-{n}_{c}\right)-r{\gamma}^{2}\right)+r\gamma {n}_{c}\right)}{{n}_{c}\left(c\beta \left(3{t}_{c}-{n}_{c}\right)-r{\gamma}^{2}\right)}.$$
- (ii)
- Consumers are single-homing and producers are multi-homing (S-M scenario) if the network effects obtained by consumers are sufficiently strong, i.e.,$${n}_{c}>\frac{{t}_{p}\left(r\gamma +c\beta \left({t}_{p}-{n}_{p}\right)\right)}{r}.$$
- (iii)
- Consumers and producers are multi-homing (M-M scenario) if the network effects obtained by consumers are sufficiently weak and the network effects obtained by producers are sufficiently strong, i.e.,$${n}_{c}<\frac{\left(2c\beta {t}_{c}-r{\gamma}^{2}\right){t}_{p}}{r\gamma +2c\beta {t}_{p}}and{n}_{p}\frac{r\gamma}{c\beta}+{t}_{p}.$$
- (iv)
- In all other scenarios, consumers and producers are single-homing (S-S scenario).

**Proof.**

## 5. Numerical Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Appendix A. Proofs

#### Appendix A.1. Proof of Proposition 1

#### Appendix A.2. Proof of Corollary 1

#### Appendix A.3. Proof of Proposition 2

#### Appendix A.4. Proof of Corollary 2

#### Appendix A.5. Proof of Proposition 3

#### Appendix A.6. Proof of Corollary 3

#### Appendix A.7. Proof of Proposition 4

#### Appendix A.8. Proof of Corollary 4

#### Appendix A.9. Proof of Proposition 5

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Parameters | |||
---|---|---|---|

${n}_{c}$ | Cross-side network effects obtained by consumers (from producers) | ${n}_{p}$ | Cross-side network effects obtained by producers (from consumers) |

${t}_{c}$ | Cost of consumer preference (transport costs) | ${t}_{p}$ | Cost of producer preference (transport costs) |

${Q}_{c}^{i}$ | Number of consumers on platform i | ${Q}_{p}^{i}$ | Number of producers on platform i |

$\beta $ | Consumer’s disutility of advertising | r | Unit advertising revenue of the platform |

V | Reservation utility for consumers | $\gamma $ | Consumer’s utility derived from high quality content |

c | Marginal cost of CQA investment | ${\pi}^{i}$ | Profit function of platform i |

Decision Variables | |||

${a}^{i}$ | Advertising level on platform i | ${\delta}^{i}$ | CQA investment on platform i |

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## Share and Cite

**MDPI and ACS Style**

Zhu, X.; Lang, M.; Dietl, H.M.
Content Quality Assurance on Media Platforms with User-Generated Content. *J. Theor. Appl. Electron. Commer. Res.* **2023**, *18*, 1660-1686.
https://doi.org/10.3390/jtaer18030084

**AMA Style**

Zhu X, Lang M, Dietl HM.
Content Quality Assurance on Media Platforms with User-Generated Content. *Journal of Theoretical and Applied Electronic Commerce Research*. 2023; 18(3):1660-1686.
https://doi.org/10.3390/jtaer18030084

**Chicago/Turabian Style**

Zhu, Xingzhen, Markus Lang, and Helmut Max Dietl.
2023. "Content Quality Assurance on Media Platforms with User-Generated Content" *Journal of Theoretical and Applied Electronic Commerce Research* 18, no. 3: 1660-1686.
https://doi.org/10.3390/jtaer18030084