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Context Sensing System Analysis for Privacy Preservation Based on Game Theory^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Single-Stage Game Analysis Based on the Extensive Form Game Formulation

#### 3.1. Problem Statement and the Extensive Form Game Formulation

#### 3.2. Payoff Function

#### 3.2.1. The User’s Payoff Function

#### 3.2.2. The Application’s Payoff Function

#### 3.2.3. The Adversary’s Payoff Function

#### 3.3. Solving and Analyzing the Nash Equilibrium

#### 3.3.1. The Solution of the Nash Equilibrium

**Proposition**

**1.**

**Proof**

**of**

**Proposition**

**1.**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**2.**

#### 3.3.2. The Analysis of the Nash Equilibrium

## 4. Repeated Game Analysis

#### 4.1. Not Concealing the Identity of the Application

#### 4.2. Concealing the Identity of the Application

## 5. Numerical Analysis

#### 5.1. Numerical Analysis of the Single-Stage Game Model

#### 5.2. Numerical Analysis of the Repeated Game Model

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**Impact of ${\mathit{k}}_{3}-{\mathit{k}}_{2}$ and ${\delta}_{a}$ on the application’s strategies.

**Figure 8.**Impact of ${\mathit{k}}_{3}-{\mathit{k}}_{2}$ and ${\delta}_{a}$ on the application’s payoffs.

Play | ${\mathit{\omega}}_{1}=({\mathit{\alpha}}_{1},{\mathit{\beta}}_{1},{\mathit{\gamma}}_{1})$ | ${\mathit{\omega}}_{2}=({\mathit{\alpha}}_{1},{\mathit{\beta}}_{1},{\mathit{\gamma}}_{2})$ | ${\mathit{\omega}}_{3}=({\mathit{\alpha}}_{1},{\mathit{\beta}}_{2},{\mathit{\gamma}}_{1})$ | ${\mathit{\omega}}_{4}=({\mathit{\alpha}}_{1},{\mathit{\beta}}_{2},{\mathit{\gamma}}_{2})$ | ${\mathit{\omega}}_{5}=({\mathit{\alpha}}_{2},{\mathit{\beta}}_{2},{\mathit{\gamma}}_{1})$ | ${\mathit{\omega}}_{6}=({\mathit{\alpha}}_{2},{\mathit{\beta}}_{2},{\mathit{\gamma}}_{2})$ | |
---|---|---|---|---|---|---|---|

Payoff | |||||||

${h}_{u}({\omega}_{i})$ | $Q(c)-{k}_{1}\phantom{\rule{0.166667em}{0ex}}Sens(c)$ | $Q(c)$ | $Q(c)$ | $Q(c)$ | 0 | 0 | |

${h}_{a}({\omega}_{i})$ | $Q(c)+({k}_{3}-{k}_{2})\phantom{\rule{0.166667em}{0ex}}Sens(c)$ | $Q(c)$ | $Q(c)$ | $Q(c)$ | 0 | 0 | |

${h}_{ad}({\omega}_{i})$ | $-C+{k}_{4}\phantom{\rule{0.166667em}{0ex}}Sens(c)$ | 0 | $-C$ | 0 | $-C$ | 0 |

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**MDPI and ACS Style**

Wang, S.; Li, L.; Sun, W.; Guo, J.; Bie, R.; Lin, K.
Context Sensing System Analysis for Privacy Preservation Based on Game Theory. *Sensors* **2017**, *17*, 339.
https://doi.org/10.3390/s17020339

**AMA Style**

Wang S, Li L, Sun W, Guo J, Bie R, Lin K.
Context Sensing System Analysis for Privacy Preservation Based on Game Theory. *Sensors*. 2017; 17(2):339.
https://doi.org/10.3390/s17020339

**Chicago/Turabian Style**

Wang, Shengling, Luyun Li, Weiman Sun, Junqi Guo, Rongfang Bie, and Kai Lin.
2017. "Context Sensing System Analysis for Privacy Preservation Based on Game Theory" *Sensors* 17, no. 2: 339.
https://doi.org/10.3390/s17020339