# Generation Mechanism of “Information Cocoons” of Network Users: An Evolutionary Game Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Construction and Analysis

#### 2.1. Description of Evolutionary Game Subjects

#### 2.2. Basic Assumptions

**Assumption 1.**

**Assumption 2.**

_{.}If the network users accept the attractive content recommended by the algorithm of the information platforms, they may suffer from addiction, cognitive dissonance, physical fatigue, and other problems, resulting in additional costs $H$. The widespread use of algorithm recommendations by information platforms for all users of the network community leads to losses of privacy for users who conflict with algorithm recommendations, which is ${R}_{2}$. And the information platforms’ behavior infringes on the privacy of the network users and needs to bear the risk, denoted as ${R}_{1}$.

**Assumption 3.**

**Assumption 4.**

#### 2.3. Model Setting

_{1}, E

_{2}, and average income $\overline{{E}_{S}}$ are

_{1}, E

_{2}, and average income $\overline{{E}_{D}}$ are

**Situation 1.**

**Situation 2.**

**Situation 3.**

#### 2.4. Analysis and Discussion

## 3. Simulation

## 4. Conclusions and Managerial Implications

#### 4.1. Conclusions

#### 4.2. Managerial Implications

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Parameter | Description |
---|---|

$S$ | Information platforms. |

$D$ | Network users. |

$p$ | The probability of information platforms using algorithm recommendation is $p$, and the probability of information platforms giving up algorithm recommendation is $1-p$. |

$q$ | The probability of network users accepting algorithm recommendation is $q$, and the probability of network users conflict algorithm recommendation is $1-q$. |

$W$ | The net incomes of information platforms give up algorithm recommendation are ${W}_{1}$, and the net incomes of network users conflict algorithm recommendation are ${W}_{2}$. |

$B$ | The additional incomes of information platforms using the algorithm recommendation are ${B}_{1}$, and the additional incomes of network users who accept algorithm recommendation are ${B}_{2}$. |

${C}_{1}$ | The losses of information platforms giving up algorithm recommendation are ${C}_{1}$ (such as users churn and competitiveness decline). |

${C}_{2}$ | The losses of network users due to information platforms giving up algorithm recommendation (such as information lag and dissatisfaction). |

$T$ | The costs of information platforms using algorithm recommendation are $T$(such as wage costs). When network users accept algorithm recommendation, the costs are ${T}_{1}$; otherwise, they are ${T}_{2},{T}_{1}{T}_{2}$. |

$L$ | When algorithm recommendation is conflicted, the additional losses of information platforms are ${L}_{1}$ (such users complaint) and the losses of network users are ${L}_{2}$ (such as aversion). |

$H$ | Information platforms use algorithm recommendation to attract network users, which will cause additional costs for network users (such as addiction and physical fatigue). |

$R$ | When information platforms use algorithm recommendation, the privacy losses of network users who conflict algorithm recommendation are ${R}_{2}$ and the risk of privacy invasion taken by information platforms is ${R}_{1}$. |

$V$ | The additional incomes of information platforms collect and process the data of network users who accept algorithm recommendation are $V$. |

The Main Strategies | $\mathbf{Information}\mathbf{Platforms}\mathbf{Choose}\mathbf{to}\mathbf{Use}\left(\mathit{p}\right)$ | $\mathbf{Information}\mathbf{Platforms}\mathbf{Choose}\mathbf{to}\mathbf{Give}\mathbf{Up}(1-\mathit{p})$ |
---|---|---|

Network users choose to accept ($q$) | $\begin{array}{c}{W}_{2}+{B}_{2}-H;\\ {W}_{1}+{B}_{1}+V-{T}_{1}\end{array}$ | $\begin{array}{c}{W}_{2}-{C}_{2};\\ {W}_{1}-{C}_{1}\end{array}$ |

Network users choose to conflict ($1-q$) | $\begin{array}{c}{W}_{2}-{L}_{2}-{R}_{2};\\ {W}_{1}-{L}_{1}-{T}_{2}-{R}_{1}\end{array}$ | $\begin{array}{c}{W}_{2};\\ {W}_{1}\end{array}$ |

Equilibrium Point | $\mathit{d}\mathit{e}\mathit{t}\mathit{J}$ | $\mathit{t}\mathit{r}\mathit{J}$ | Results |
---|---|---|---|

$\left(\mathrm{0,0}\right)$ | ${C}_{2}({L}_{1}+{T}_{2}+{R}_{1})$ | $-{C}_{2}-({L}_{1}+{T}_{2}+{R}_{1})$ | It is a stable point under any conditions |

$\left(\mathrm{0,1}\right)$ | ${C}_{2}\left({B}_{1}+{C}_{1}-{T}_{1}+V\right)$ | ${B}_{1}+{C}_{1}-{T}_{1}+V+{C}_{2}$ | It is an unstable point under any conditions |

$\left(\mathrm{1,0}\right)$ | $\left({L}_{1}+{T}_{2}+{R}_{1}\right)\times $ $\left({B}_{2}-H+{R}_{2}+{L}_{2}\right)$ | $\left({L}_{1}+{T}_{2}+{R}_{1}\right)+$ $\left({B}_{2}-H+{R}_{2}+{L}_{2}\right)$ | It is an unstable point under any conditions |

$\left(\mathrm{1,1}\right)$ | $\left({B}_{1}+{C}_{1}-{T}_{1}+V\right)\times $ $\left({B}_{2}-H+{R}_{2}+{L}_{2}\right)$ | $-\left({B}_{1}+{C}_{1}-{T}_{1}+V\right)$ $-\left({B}_{2}-H+{R}_{2}+{L}_{2}\right)$ | When ${T}_{1}<{B}_{1}+{C}_{1}+V$ and $H<{B}_{2}+{L}_{2}+{R}_{2}$ it is a stable point; otherwise, a saddle point or unstable point |

Equilibrium | $\mathit{d}\mathit{e}\mathit{t}\mathit{J}$ | $\mathit{t}\mathit{r}\mathit{J}$ | Stability |
---|---|---|---|

$\left(\mathrm{0,0}\right)$ | $+$ | $-$ | $ESS$ |

$\left(\mathrm{0,1}\right)$ | $-$ | indetermination | instability |

$\left(\mathrm{1,0}\right)$ | $-$ | indetermination | instability |

$\left(\mathrm{1,1}\right)$ | $+$ | $+$ | instability |

$({p}^{\mathrm{*}},{q}^{\mathrm{*}})$ | $0$ | $-$ | saddle point |

Equilibrium | $\mathit{d}\mathit{e}\mathit{t}\mathit{J}$ | $\mathit{t}\mathit{r}\mathit{J}$ | Stability |
---|---|---|---|

$\left(\mathrm{0,0}\right)$ | $+$ | $-$ | $ESS$ |

$\left(\mathrm{0,1}\right)$ | $-$ | indetermination | instability |

$\left(\mathrm{1,0}\right)$ | $-$ | indetermination | instability |

$\left(\mathrm{1,1}\right)$ | $+$ | $+$ | instability |

$({p}^{\mathrm{*}},{q}^{\mathrm{*}})$ | $0$ | indetermination | saddle point |

Equilibrium | $\mathit{d}\mathit{e}\mathit{t}\mathit{J}$ | $\mathit{t}\mathit{r}\mathit{J}$ | Stability |
---|---|---|---|

$\left(\mathrm{0,0}\right)$ | $+$ | $-$ | $ESS$ |

$\left(\mathrm{0,1}\right)$ | $+$ | $+$ | instability |

$\left(\mathrm{1,0}\right)$ | $+$ | $+$ | instability |

$\left(\mathrm{1,1}\right)$ | $+$ | $-$ | $ESS$ |

$({p}^{\mathrm{*}},{q}^{\mathrm{*}})$ | $0$ | $+$ | saddle point |

Parameter | ${\mathit{W}}_{1}$ | ${\mathit{W}}_{2}$ | ${\mathit{B}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{L}}_{1}$ | ${\mathit{L}}_{2}$ | $\mathit{H}$ | ${\mathit{T}}_{2}$ | ${\mathit{R}}_{1}$ | ${\mathit{R}}_{2}$ | $\mathit{V}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Value | 10 | 9 | 5 | 3 | 3 | 2.5 | 2 | 5 | 3.5 | 2 | 2 | 4 | 2 |

Parameter | ${\mathit{W}}_{1}$ | ${\mathit{W}}_{2}$ | ${\mathit{B}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{L}}_{1}$ | ${\mathit{L}}_{2}$ | ${\mathit{T}}_{1}$ | ${\mathit{T}}_{2}$ | ${\mathit{R}}_{1}$ | ${\mathit{R}}_{2}$ | $\mathit{V}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Value | 10 | 9 | 5 | 3 | 3 | 2.5 | 2 | 5 | 5 | 2 | 2 | 4 | 2 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Cai, Y.; Zhao, M.; Zhou, Y.
Generation Mechanism of “Information Cocoons” of Network Users: An Evolutionary Game Approach. *Systems* **2023**, *11*, 414.
https://doi.org/10.3390/systems11080414

**AMA Style**

Zhang X, Cai Y, Zhao M, Zhou Y.
Generation Mechanism of “Information Cocoons” of Network Users: An Evolutionary Game Approach. *Systems*. 2023; 11(8):414.
https://doi.org/10.3390/systems11080414

**Chicago/Turabian Style**

Zhang, Xing, Yongtao Cai, Mengqiao Zhao, and Yan Zhou.
2023. "Generation Mechanism of “Information Cocoons” of Network Users: An Evolutionary Game Approach" *Systems* 11, no. 8: 414.
https://doi.org/10.3390/systems11080414