# Can the Conditional Rebate Strategy Work? Signaling Quality via Induced Online Reviews

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## Abstract

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## 1. Introduction

- Under what conditions will online sellers adopt a conditional rebate strategy to obtain positive online reviews?
- When using such rebates, what is the optimal cost to sellers to maximize profit?
- How does the conditional rebate strategy affect different kinds of sellers’ profits?

## 2. Literature Review

## 3. Models

#### 3.1. The Online Sellers

#### 3.2. Information Updates about Quality

#### 3.3. Consumers’ Decisions

#### 3.4. Gaming

## 4. Equilibrium Analysis

#### 4.1. Benchmark Case without the Rebate Strategy

**Proposition 1.**

#### 4.2. Benchmark Case with Rebate Strategy

**Proposition 2.**

**Corollary 1.**

**Corollary 2.**

**Proposition 3.**

**Corollary 3.**

## 5. Numerical Study

#### 5.1. Effect of $\rho $ on the Equilibrium Outcomes

#### 5.2. Effect of p on Equilibrium Outcomes

#### 5.3. Comparison under Parameter Combinations

## 6. Conclusions and Implications

#### 6.1. Conclusions

#### 6.2. Implications

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Proofs of Propositions

**Proof of Proposition 1.**

**Proof of Proposition 2.**

**Proof of Corollary 1.**

**Proof of Corollary 2.**

**Proof of Proposition 3.**

**Proof of Corollary 3.**

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Notation | Description |
---|---|

j | Product type, $j\in \{h,l\}$ |

${q}_{j}$ | j-type product quality |

$\alpha $ | Probability that the product is type h |

$1-\alpha $ | Probability that the product is type l |

${s}_{j}$ | Signal type |

$\rho $ | Sensitivity factor of consumers to rebate for positive reviews |

$\lambda $ | Coefficient of improvement in information accuracy brought by sales of the l-type product in the first stage |

$\beta $ | Cost of rebate for positive reviews |

v | Consumers’ baseline utility |

$E\left[q\right]$ | Quality of products expected by consumers |

p | Price of product |

U | Consumer utility |

${d}_{ij}$$({d}_{ij}^{n})$ | Demand for the j-type product at period i with (without) the rebate strategy |

${\Pi}_{j}$$({\Pi}_{j}^{n})$ | j-type seller’s total profit with (without) rebate strategy |

${\mathit{q}}_{\mathit{h}}$ | ${\mathit{q}}_{\mathit{l}}$ | p | $\mathit{\rho}$ | |
---|---|---|---|---|

Case 1 $\alpha $ = 0.2 | 0.8 | 0.4 | 1 | 0.8 |

Case 2 $\alpha $ = 0.6 | 0.8 | 0.4 | 1 | 0.8 |

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## Share and Cite

**MDPI and ACS Style**

Xiao, L.; Qian, C.; Wang, C.; Wang, J.
Can the Conditional Rebate Strategy Work? Signaling Quality via Induced Online Reviews. *J. Theor. Appl. Electron. Commer. Res.* **2024**, *19*, 54-72.
https://doi.org/10.3390/jtaer19010004

**AMA Style**

Xiao L, Qian C, Wang C, Wang J.
Can the Conditional Rebate Strategy Work? Signaling Quality via Induced Online Reviews. *Journal of Theoretical and Applied Electronic Commerce Research*. 2024; 19(1):54-72.
https://doi.org/10.3390/jtaer19010004

**Chicago/Turabian Style**

Xiao, Lu, Chen Qian, Chaojie Wang, and Jun Wang.
2024. "Can the Conditional Rebate Strategy Work? Signaling Quality via Induced Online Reviews" *Journal of Theoretical and Applied Electronic Commerce Research* 19, no. 1: 54-72.
https://doi.org/10.3390/jtaer19010004