# Group Buying-Based Data Transmission in Flying Ad-Hoc Networks: A Coalition Game Approach

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## Abstract

**:**

## 1. Introduction

- A resource allocation optimization method based on distributed data content is proposed, where different data content is considered to transmit to UAVs which have corresponding data requirements. The designed utility function based on data transmission probability can reflect both link qualities and the efficiency of resource transmission. This provides theoretical support for the UAVs’ coalition selections and the formation of internal stable structures.
- We propose a coalition game framework to solve resource allocation and data transmission problems. In the framework, coalitional graph game characterizes the inner coalition structure (transmission mechanism). Data resource allocation of UAVs is analyzed in coalition formation game (CFG). Both games are proven to have stable solutions, indicating the effectiveness of our proposed model.
- A cooperative coalition selection mechanism is proposed to improve the performance of system model. CO-CSA and PO-CSA are designed to execute cooperative exchange mechanism. Simulation results show that both CO-CSA and PO-CSA achieve better performance than Onetime-CSA. In addition, the performance of CO-CSA is better than PO-CSA, while PO-CSA converges in less time.

## 2. System Model and Problem Formulation

#### 2.1. System Model

#### 2.2. Problem Formulation

## 3. Coalitional Graph Game for Data Transmission

**Definition**

**1**

**(Coalitional**

**graph**

**game**

**[15]).**

- $\mathcal{N}$ is a set of all nodes (including central UAV).
- ε is the set of all edges (UAV-to-UAV links). For any $i,j\in \mathcal{N}$, we say the link from i to j exists, if ${e}_{i,j}\in \epsilon $.
- ${C}_{n}$ is the available coalition selections for each $n\in \mathcal{N}$, let ${c}_{n}\in {C}_{n}$ denote the coalition selection for n.
- $U{1}_{n}$ represents the utility function of UAV n while playing its strategy.

**Definition**

**2**

**(Local**

**Nash**

**network**

**[19]).**

Algorithm 1 Throughput maximization network formation algorithm. |

(1) Input $C{O}_{{c}_{n}}$, set $\mathcal{K}=\left\{{\mathrm{ch}}_{{c}_{n}}\right\}$. (2) while: All UAVs in coalition $C{O}_{{c}_{n}}$ are connected considering data content s, i.e., $\mathcal{K}=C{O}_{{c}_{n}}^{s}$.1: Find $(i,j)=argmin{d}_{i,j}$, $j\in \mathcal{K}$, UAV $i\in K1$, where $K1=\{i\in C{O}_{{c}_{n}}^{s}:i\notin \mathcal{K}\}$.2: Find UAV m if $m=argmaxU{1}_{{a}_{i}}\left(G\right)$ where ${a}_{i}=m$.3: Offer UAV i and UAV m a new link ${e}_{i,m}$. Add i and ${e}_{i,m}$ to $\mathcal{K}$ and ${\epsilon}_{s}^{n}$, respectively.End(3) Output routing link ${\epsilon}_{s}^{n}$ and UAV n’s current coalition $C{O}_{{c}_{n}}$’s throughput $U{1}_{n}\left(G\right)$. |

## 4. Coalition Formation Game for Resources Allocation based on Group Buying

**Definition**

**3**

**(Coalition**

**formation**

**game,**

**CFG**

**[15]).**

#### 4.1. Game Model

**Definition**

**4**

**(Pareto**

**order**

**[23]).**

**Definition**

**5**

**(Coalition**

**order).**

**Definition**

**6**

**(Coalition**

**selection**

**mechanism).**

#### 4.2. Analysis of the Stable Coalition Partition

**Definition**

**7**

**(Stable**

**coalition**

**partition**

**[14]).**

**Theorem**

**1.**

**Proof.**

**Definition**

**8**

**(Exact**

**potential**

**game**

**[27]).**

**EPG**) and has at least one Nash equilibrium (NE) point; the function is called potential function.

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

#### 4.3. Algorithm Design

Algorithm 2 Coalition order/(Pareto order) based coalition selection algorithm, CO-CSA/(PO-CSA) |

Step 1: Initialize UAVs’ state strategies ${\left\{{c}_{n}\right\}}_{n\in \mathcal{N}}$ considering data content s.Loop:$k=1,2,\dots ,$ IterationMaxStep 2: Select one UAV randomly, say i. $CO\leftarrow C{O}_{{c}_{i}}$.Step 3: Input $C{O}_{{c}_{i}}$ into Algorithm 1 and obtain ${\epsilon}_{s}$. Calculate $U{2}_{i}({c}_{i}\left(j\right),{c}_{-i}\left(j\right))$ according to Equation (8).Step 4: UAV i generate a new strategy $\tilde{{c}_{i}}\in {C}_{i}/\left\{{c}_{i}\left(j\right)\right\}$. $C{O}^{\prime}\leftarrow C{O}_{\tilde{{c}_{i}}}\cup i$.Step 5: Input $C{O}^{\prime}$ into Algorithm 1 and obtain ${\epsilon}_{s}$. Calculate $U{2}_{i}(\tilde{{c}_{i}}\left(j\right),{c}_{-i}\left(j\right))$ according to Equation (8).Step 6: UAV i update strategy with coalition order/ (Pareto order) according to Equation (10)/(Equation (9)), and the update probability is given as follows:
$$P({c}_{i}(j+1)={c}_{i}\left(j\right))=\frac{exp\left\{\beta U{2}_{i}({c}_{i}\left(j\right),{c}_{-i}\left(j\right))\right\}}{exp\left\{\beta U{2}_{i}({c}_{i}\left(j\right),{c}_{-i}\left(j\right))\right\}+exp\left\{\beta U{2}_{i}(\tilde{{c}_{i}},{c}_{-i}\left(j\right))\right\}}.$$
Step 7: Update ${c}_{-i}(j+1)={c}_{-i}\left(j\right)$.End loop: |

## 5. Simulation Results and Discussion

#### 5.1. Basic Performance

#### 5.2. Different Orders and Contrast Algorithms

#### 5.3. Convergence Performance

#### 5.4. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 5.**Performance comparison of algorithms based on (

**a**) data overlap degree and (

**b**) border length of scenario.

**Figure 6.**The average convergence times of different numbers of users and data with different methods. (

**a**) The average convergence times considering UAV amount. (

**b**) The total data throughout considering border length of scenario.

Number of UAVs (N) | Mean (Mbps) | Variance (Mbps) | Confidence Interval (Mbps) |
---|---|---|---|

14 | 52.07 | 8.74 | (50.33, 53.80) |

16 | 61.02 | 8.30 | (59.38, 62.67) |

18 | 70.77 | 8.99 | (68.98, 72.55) |

20 | 70.77 | 9.96 | (78.45, 82.40) |

22 | 89.93 | 10.16 | (87.92, 91.95) |

24 | 102.23 | 11.23 | (100.00, 104.46) |

26 | 110.14 | 11.32 | (107.90, 112.39) |

28 | 120.55 | 11.65 | (118.24, 122.87) |

30 | 130.73 | 12.35 | (128.28, 133.18) |

32 | 140.32 | 12.29 | (137.88, 142.76) |

34 | 149.16 | 12.70 | (146.64, 151.68) |

Overlap Degree ($\mathit{Od}$) | Mean (Mbps) | Variance (Mbps) | Confidence Interval (Mbps) |
---|---|---|---|

0.3 | 35.81 | 6.78 | (34.46, 37.15) |

0.35 | 45.75 | 8.52 | (44.06, 47.44) |

0.4 | 56.79 | 9.82 | (54.84, 58.74) |

0.45 | 69.18 | 9.10 | (67.37, 70.99) |

0.5 | 78.04 | 9.71 | (76.11, 79.97) |

0.55 | 93.99 | 10.12 | (91.98, 96.00) |

0.6 | 106.93 | 9.50 | (105.05, 108.82) |

0.65 | 119.03 | 10.51 | (116.94, 121.12) |

0.7 | 133.84 | 11.03 | (131.65, 136.03) |

0.75 | 147.02 | 10.84 | (144.87, 149.17) |

0.8 | 161.34 | 10.28 | (159.30, 163.38) |

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**MDPI and ACS Style**

Ruan, L.; Chen, J.; Guo, Q.; Zhang, X.; Zhang, Y.; Liu, D.
Group Buying-Based Data Transmission in Flying Ad-Hoc Networks: A Coalition Game Approach. *Information* **2018**, *9*, 253.
https://doi.org/10.3390/info9100253

**AMA Style**

Ruan L, Chen J, Guo Q, Zhang X, Zhang Y, Liu D.
Group Buying-Based Data Transmission in Flying Ad-Hoc Networks: A Coalition Game Approach. *Information*. 2018; 9(10):253.
https://doi.org/10.3390/info9100253

**Chicago/Turabian Style**

Ruan, Lang, Jin Chen, Qiuju Guo, Xiaobo Zhang, Yuli Zhang, and Dianxiong Liu.
2018. "Group Buying-Based Data Transmission in Flying Ad-Hoc Networks: A Coalition Game Approach" *Information* 9, no. 10: 253.
https://doi.org/10.3390/info9100253