# Research on the Product Positioning Strategy of the Independent Seller under Platform Encroachment

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Platform Encroachment

#### 2.2. Product Positioning

## 3. Modeling and Analysis

#### 3.1. In the Case of Non-Encroachment

**Lemma**

**1.**

**Proposition**

**1.**

#### 3.2. In the Case of Encroachment

**Lemma**

**2.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proposition**

**4.**

#### 3.3. O’s Encroachment Strategy

**Proposition**

**5.**

**Proposition**

**6.**

#### 3.4. Equilibrium Strategy Analysis

**Proposition**

**7.**

#### 3.5. Consumer Surplus and Social Welfare

**Proposition**

**8.**

## 4. Numerical Simulation

#### 4.1. Multi-Agent Model Construction

#### 4.1.1. Consumer Behavior

#### 4.1.2. Decision Makers’ Behavior

#### 4.2. Simulation Results and Analysis

#### 4.2.1. The Impact of σ on S’s Vertical Positioning

**Observation**

**1.**

#### 4.2.2. The Impact of σ on S’s Horizontal Positioning

**Observation**

**2.**

#### 4.2.3. The Impact of σ on O’s Encroachment Strategy

**Observation**

**3.**

## 5. Three Extensions

#### 5.1. Positive Production Cost

**Proposition**

**9.**

**Proposition**

**10.**

#### 5.2. Pricing Decision Order

**Proposition**

**11.**

#### 5.3. O’s Consumer Surplus Concern

**Proposition**

**12.**

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Consumer market segmentation (

**a**) in the case of non-encroachment and (

**b**) in the case of encroachment.

**Figure 9.**Joint effect of σ and ${q}_{j}$ on S’s horizontal positioning (c = 0.05, r = 0.1, δ = 1.5).

**Figure 10.**Joint effect of σ and ${q}_{j}$ on O’s encroachment strategy (c = 0.01, r = 0.9, δ = 1.1): (

**a**) encroachment on the low-quality category; (

**b**) encroachment on the high-quality category.

**Figure 11.**Impact of μ on O’s encroachment strategy (${q}_{j}\text{}$= 9, r = 0.99, t = 1): (

**a**) μ = 0; (

**b**) μ = 1; (

**c**) μ = 4.

Symbols | Definition |
---|---|

α | Degree of vertical differentiation between category L and category H. Category L corresponds to the low-quality category, while category H corresponds to the high-quality category. |

r | Platform commission rate. |

t | The utility loss per unit distance, when a consumer purchases a product that is not their ideal preference. |

δ | The consumer preference for platform self-owned products. |

c | The horizontal differentiation cost per unit. |

${q}_{j}$ | The category j’s quality ($j\in \{L,\text{}H\}$). |

${d}_{j}$ | The degree of horizontal differentiation between Sj and Oj. S and O indicate the independent seller and platform owner, respectively. |

${x}_{ij}$ | The distance between the consumer’s ideal and product ij ($i\in \{O,\text{}S\}$). |

${p}_{ij}^{N}$(${p}_{ij}^{E}$) | The retail price of product ij under strategy N (strategy E). Strategy N indicates that O does not encroach, while strategy E indicates that O encroaches. |

${U}_{ij}$ | The utility obtained by the consumer from purchasing product ij. |

${D}_{ij}^{N}$(${D}_{ij}^{E}$) | The market demand of product ij under strategy N (strategy E). |

${\pi}_{ij}^{N}$(${\pi}_{ij}^{E}$) | The i’s profit when S chooses to sell category j and O adopts strategy N (strategy E). |

${CS}^{N}$(${CS}^{E}$) | The consumer surplus under strategy N (strategy E). |

${SW}^{N}$(${SW}^{E}$) | The social welfare under strategy N (strategy E). |

σ | The heterogeneity of consumers’ ideal preferences. |

k | The cost per unit of product quality. |

μ | The degree of O’s consumer surplus concern. |

O | S | |
---|---|---|

L | H | |

N | ${{\pi}_{SL}^{N}}^{*}=\frac{{{q}_{L}}^{2}(1-r)}{2t}$ | ${{\pi}_{SH}^{N}}^{*}=\frac{{\alpha}^{2}{{q}_{L}}^{2}(1-r)}{2t}$ |

${{\pi}_{OL}^{N}}^{*}=\frac{{{q}_{L}}^{2}r}{2t}$ | ${{\pi}_{OH}^{N}}^{*}=\frac{{\alpha}^{2}{{q}_{L}}^{2}r}{2t}$ | |

E | ${{\pi}_{SL}^{E}}^{*}=\frac{{c(M}_{1}+{q}_{L}{M}_{2})}{49(1-r)t}$ | ${{\pi}_{SH}^{E}}^{*}=\frac{{c(M}_{1}+\alpha {q}_{L}{M}_{2})}{49(1-r)t}$ |

${{\pi}_{OL}^{E}}^{*}=\frac{6({M}_{3}+{q}_{L}{M}_{4}+{{q}_{L}}^{2}{M}_{5})}{2401{(1-r)}^{2}t}$ | ${{\pi}_{OH}^{E}}^{*}=\frac{6({M}_{3}+\alpha {q}_{L}{M}_{4}+{\alpha}^{2}{{q}_{L}}^{2}{M}_{5})}{2401{(1-r)}^{2}t}$ |

N | E | |
---|---|---|

${{d}_{j}}^{*}$ | — | $\frac{24c\left(17-r\right)-{q}_{j}{M}_{12}}{49(1-r)t}$ |

${{p}_{Sj}}^{*}$ | $\frac{{q}_{j}(1+k-r)}{2(1-r)}$ | $\frac{12c+7k{q}_{j}}{7(1-r)}$ |

${{p}_{Oj}}^{*}$ | — | $\frac{2c(41+5r)+{q}_{j}{M}_{13}}{49(1-r)}$ |

${{\pi}_{Sj}}^{*}$ | $\frac{{{q}_{j}}^{2}{(-1+k+r)}^{2}}{2(1-r)t}$ | $\frac{c(12c\left(-17+r\right)-{q}_{j}{M}_{14})}{49(1-r)t}$ |

${{\pi}_{Oj}}^{*}$ | $\frac{{{q}_{j}}^{2}r(-1-k+r)(-1+k+r)}{2{(1-r)}^{2}t}$ | $\frac{2({M}_{15}+{{q}_{j}}^{2}{M}_{16}-{q}_{j}{M}_{17})}{2401{(-1+r)}^{2}t}$ |

E | |
---|---|

${{d}_{j}}^{*}$ | $\frac{c{(-35+r)}^{2}}{147t(1-r)}+\frac{{q}_{j}(3\delta -17)}{7t}$ |

${{p}_{Sj}}^{*}$ | $\frac{c(35-r)}{21(1-r)}$ |

${{p}_{Oj}}^{*}$ | $\frac{c(35-r)(7+r)}{147(1-r)}+\frac{4{q}_{j}(\delta -1)}{7}$ |

${{\pi}_{Sj}}^{*}$ | $\frac{c(c{(-35+r)}^{2}+42{q}_{j}(-1+r)(17-3\delta ))}{294(-1+r)t}$ |

${{\pi}_{Oj}}^{*}$ | $\frac{{M}_{21}+{q}_{j}{M}_{22}+{{q}_{j}}^{2}{M}_{23}}{\mathrm{43,218}{(-1+r)}^{2}t}$ |

N | E | |
---|---|---|

${{d}_{j}}^{*}$ | — | $\frac{12c(-2+\mu )(-17+r+8\mu )+{q}_{j}(-1+r)(-7+4\mu )(-17+3\delta +8\mu )}{(1-r)t{(7-4\mu )}^{2}}$ |

${{p}_{Sj}}^{*}$ | $\frac{{q}_{j}}{2}$ | $\frac{6c(-2+\mu )}{(1-r)(-7+4\mu )}$ |

${{p}_{Oj}}^{*}$ | — | $\frac{4{q}_{j}(-1+r)(-1+\delta )(-1+\mu )(-7+4\mu )+2c(-41-5r+61\mu +2r\mu -20{\mu}^{2})}{(-1+r){(7-4\mu )}^{2}}$ |

${{\pi}_{Sj}}^{*}$ | $\frac{{{q}_{j}}^{2}(1-r)}{2t}$ | $\frac{c(6c(-2+\mu )(-17+r+8\mu )+{q}_{j}(-1+r)(-7+4\mu )(-17+3\delta +8\mu ))}{(-1+r)t{(7-4\mu )}^{2}}$ |

${{\pi}_{Oj}}^{*}$ | $\frac{{{q}_{j}}^{2}(2r+\mu )}{4t}$ | $\frac{6({{q}_{j}}^{2}{M}_{24}-{q}_{j}{M}_{25}+{M}_{26})}{{(-1+r)}^{2}t{(7-4\mu )}^{4}}$ |

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**MDPI and ACS Style**

Wang, Z.; Yang, T.
Research on the Product Positioning Strategy of the Independent Seller under Platform Encroachment. *Systems* **2024**, *12*, 36.
https://doi.org/10.3390/systems12010036

**AMA Style**

Wang Z, Yang T.
Research on the Product Positioning Strategy of the Independent Seller under Platform Encroachment. *Systems*. 2024; 12(1):36.
https://doi.org/10.3390/systems12010036

**Chicago/Turabian Style**

Wang, Ziyan, and Tianjian Yang.
2024. "Research on the Product Positioning Strategy of the Independent Seller under Platform Encroachment" *Systems* 12, no. 1: 36.
https://doi.org/10.3390/systems12010036