# The Impact of Return Shipping Insurance on a Retailer Based on Restricting Rights

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Problem Description

- (1)
- Scenario NN: Both the insurer and the retailer do not have the restricting right. In this case, the insurer decides the premium m. Then, the retailer decides the retail price p and whether to purchase RSI. Finally, consumers make their purchase and return decisions.
- (2)
- Scenario NR: The insurer does not have the restricting right, whereas the retailer has the restricting right. In this case, the insurer decides the premium m. Then, the retailer decides the retail price p, and whether to purchase RSI and restrict uninformed consumers from buying the product. Finally, consumers make their purchase and return decisions.
- (3)
- Scenario RN: The insurer has the restricting right, whereas the retailer does not have the restricting right. In this case, the insurer restricts uninformed consumers from obtaining RSI and decides the premium m. Then, the retailer decides the retail price p and whether to purchase RSI. Finally, consumers make their purchase and return decisions.
- (4)
- Scenario RR: Both the insurer and the retailer have the restricting right. In this case, the insurer restricts uninformed consumers from obtaining RSI and decides the premium m. Then, the retailer decides the retail price p and whether to purchase RSI and restrict uninformed consumers from buying the product. Finally, consumers make their purchase and return decisions.

## 4. Equilibrium Analysis

#### 4.1. No Insurance–Benchmark Case (Scenario N)

**Proposition 1**.

#### 4.2. Both the Insurer and the Retailer Do Not Have the Restricted Right (Scenario NN)

**Proposition 2**.

**Proposition 3**.

#### 4.3. Only the Retailer Has the Restricted Right (Scenario NR)

**Proposition 4**.

**Proposition 5**.

#### 4.4. Only the Insurer Has the Restricted Right (Scenario RN)

**Proposition 6**.

**Proposition 7**.

#### 4.5. Both the Insurer and the Retailer Do Not Have the Restricted Right (Scenario RR)

**Proposition 8**.

**Proposition 9**.

## 5. 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 Proposition 2**.

**Proof of Proposition 3**.

**Proof of Proposition 4**.

**Proof of Proposition 5**.

**Proof of Proposition 6**.

**Proof of Proposition 7**.

**Proof of Proposition 8**.

**Proof of Proposition 9**.

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**Figure 2.**Seller’s optimal decision in scenario NR ($c=0.4,\theta =0.6,{\lambda}_{l}=0.4,{\lambda}_{h}=0.5,\beta =2,$ $h=0.048,s=0.1,k=0.0002$); (

**a**) retailer’s restricting decision in scenario NR; (

**b**) the optimal price changes in scenario NR.

**Figure 3.**The optimal premium changes in scenario NR ($c=0.4,\theta =0.6,{\lambda}_{l}=0.4,{\lambda}_{h}=0.5,$ $\beta =2,h=0.048,k=0.0002$).

**Figure 4.**Seller’s pricing strategy in scenario RN ($c=0.4,\theta =0.6,{\lambda}_{l}=0.4,{\lambda}_{h}=0.6,\beta =2,h=0.1$).

**Figure 5.**The premium changes in s in scenario RN ($c=0.4,\theta =0.6,{\lambda}_{l}=0.4,{\lambda}_{h}=0.6,\beta =2,$ $h=0.048$).

**Figure 6.**Seller’s pricing strategy in scenario RR ($c=0.4,\theta =0.6,{\lambda}_{l}=0.4,{\lambda}_{h}=0.6,\beta =2,$ $h=0.1,k=0.0002$).

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## Share and Cite

**MDPI and ACS Style**

Yang, X.; Dai, X.; Liu, Z.
The Impact of Return Shipping Insurance on a Retailer Based on Restricting Rights. *J. Theor. Appl. Electron. Commer. Res.* **2023**, *18*, 706-724.
https://doi.org/10.3390/jtaer18010036

**AMA Style**

Yang X, Dai X, Liu Z.
The Impact of Return Shipping Insurance on a Retailer Based on Restricting Rights. *Journal of Theoretical and Applied Electronic Commerce Research*. 2023; 18(1):706-724.
https://doi.org/10.3390/jtaer18010036

**Chicago/Turabian Style**

Yang, Xingyi, Xiaopei Dai, and Zhenyu Liu.
2023. "The Impact of Return Shipping Insurance on a Retailer Based on Restricting Rights" *Journal of Theoretical and Applied Electronic Commerce Research* 18, no. 1: 706-724.
https://doi.org/10.3390/jtaer18010036