# Conversion of Dual-Use Technology: A Differential Game Analysis under the Civil-Military Integration

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## Abstract

**:**

## 1. Introduction

## 2. Model Design

#### Stochastic Differential Game Models

## 3. Equilibrium Analysis

#### 3.1. Resolving Models of Spin-Off

#### 3.2. Resolving Models of Spin-In

#### 3.3. Resolving Models of Mix

## 4. Comparative Analysis of Equilibrium Results

#### 4.1. Comparative Analysis of Equilibrium Results of Optimal Effort Level

#### 4.2. Comparative Analysis of Equilibrium Results of Optimal Revenue

#### 4.3. Dual-Use Technology Development

## 5. Simulation and Discussion

#### 5.1. Generic Simulation

#### 5.2. Dual-Use Technology Development in Three Modes

#### 5.3. Individual and Total Revenue in Three Modes

#### 5.4. Revenue Comparison between Military and Civil Firms

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Data Availability

## References

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**Figure 3.**(

**a**) Military revenue changes with time; (

**b**) civilian revenue changes with time; (

**c**) total revenue changes with time.

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

M | A single military firm |

C | A single civil firm |

E(t) | The effort level of dual-use technology conversion |

c(t) | Conversion cost |

K(t) | Dual-use technologies level |

$\mu $ | Cost coefficients |

$\alpha \text{}\mathrm{and}\text{}\beta $ | Coefficient of technological innovation capability of military and civilian firms |

$\delta $ | The attenuation coefficient of dual-use technology |

Q(t) | Total revenue of dual-use technology conversion |

$\lambda $ | Coefficient of military and civilian firms on the national defense demand |

$\theta $ | Coefficient of economic demand |

t | At time t |

$\rho $ | The discount rate of dual-use technology |

$\pi $ | The revenue distribution coefficient of civil firm |

$\eta $ | Subsidy of dual-use technology conversion |

J | Objective function |

V | Optimal revenue function |

E(K(t)) | Expectation |

D(K(t)) | Variance |

$f\left(x\right)$ | A quadratic continuous differential function |

B(t) | Brownian motion |

z(t) | Standard Wiener process |

$\epsilon $ | Random interference factors |

Notation | $\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathit{\rho}$ | $\mathit{\delta}$ | $\mathit{\lambda}$ | $\mathit{\theta}$ | ${\mathit{\mu}}_{\mathit{M}}\text{}$ | ${\mathit{\mu}}_{\mathit{C}}\text{}$ | $\mathit{\pi}$ | $\mathit{\eta}$ |
---|---|---|---|---|---|---|---|---|---|---|

Initialization Settings | 0.8 | 0.6 | 0.95 | 0.1 | 0.7 | 0.6 | 0.5 | 0.5 | 0.5 | 0.333 |

Spin-Off | Spin-In | Mix | |
---|---|---|---|

${E}_{M}$ | 1.690 | 1.690 | 3.381 |

${E}_{C}$ | 1.443 | 2.536 | 2.886 |

${V}_{M}$ | 0.619K + 1.848 | 0.619K + 2.075 | 0.619K + 2.136 |

${V}_{C}$ | 0.619K + 2.052 | 0.619K + 2.324 | 0.619K + 2.136 |

V | 1.238K + 3.90 | 1.238K + 4.31 | 1.238K + 4.271 |

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**MDPI and ACS Style**

Cao, X.; Yang, X.; Zhang, L.
Conversion of Dual-Use Technology: A Differential Game Analysis under the Civil-Military Integration. *Symmetry* **2020**, *12*, 1861.
https://doi.org/10.3390/sym12111861

**AMA Style**

Cao X, Yang X, Zhang L.
Conversion of Dual-Use Technology: A Differential Game Analysis under the Civil-Military Integration. *Symmetry*. 2020; 12(11):1861.
https://doi.org/10.3390/sym12111861

**Chicago/Turabian Style**

Cao, Xia, Xiaojun Yang, and Lupeng Zhang.
2020. "Conversion of Dual-Use Technology: A Differential Game Analysis under the Civil-Military Integration" *Symmetry* 12, no. 11: 1861.
https://doi.org/10.3390/sym12111861