# FollowMe: One Social Importance-Based Collaborative Scheme in MONs
## Preliminaries
### Signal Game Model Based on Social Importance  
In an MON composed of portable devices, the behavior of nodes reflects certain social attributes due to the sociality of carriers. In addition, nodes are more willing to imitate those of high social importance. Therefore, we reflect the sociality of nodes by introducing the social importance of nodes into game procedure.  
**Social Importance:** We employ the Degree Centrality (DC) [17] to measure the social importance of nodes. The DC of a node is the number of neighbors it has. In general, higher DC signifies higher social importance. Mathematically, let \(DC_{x}\) denote the DC of node \(x\); thus, we have \(DC_{x}=K_{x}/\left(N-1\right)\), where \(K_{x}\) denotes the number of neighbors of node \(x\) and \(N\) is the number of nodes in the network. This enables us to evaluate the social importance of nodes. Suppose node \(y\) is one of the neighbors of \(x\), with its social importance \(SI_{y}\) being \(SI_{y}=DC_{y}/\sum_{y\in\Omega_{x}}DC_{x}\), where \(\Omega_{x}\) is the set of neighbors of \(x\). Subsequently, the average social importance of the neighbors of \(x\) is \(\overline{SI}=\sum_{y\in\Omega_{x}}SI_{y}/k_{x}\). Finally, we denote \(x\) as a node with high social importance if \(SI_{x}>\overline{SI}\).  
**Signal Game Model:** In game theory, a signal game is a dynamic game with incomplete information between two participants: a signal sender S and a receiver R. The game process can be summarized as follows:  
1. The sender is assumed to be one type \(t_{i}\) from a set \(T=\{t_{1},t_{2},...,t_{k}\}\); for all of the types, the probability \(p(t_{i})>0\) and their sum equals 1.
2. The sender observes the type \(t_{i}\) and selects a signal \(m_{i}\) from the signal set \(M=\{m_{1},m_{2},...,m_{l}\}\).
3. After viewing the signal \(m_{i}\) (but the receiver cannot see the type \(t_{i}\)), it selects an action \(a_{i}\) from the action set \(A=\{a_{1},a_{2},...,a_{j}\}\).
4. The sender has a bonus \(u_{s}\{t_{i},m_{i},a_{i}\}\) and that of the receiver is \(u_{r}\{t_{i},m_{i},a_{i}\}\). In this study, we assume there are two types of nodes: cooperative and non-cooperative, and set \(t_{1}=cooperative\) and \(t_{2}=noncooperative\). If one of the nodes belongs to \(t_{1}\), it participates in the forwarding process with a probability \(\theta\); otherwise, \(1-\theta\). In addition, based on the social attributes of nodes, they can select signals \(m_{1}\) or \(m_{2}\) to send, where \(m_{1}\) and \(m_{2}\) indicate nodes of high and low social importance, respectively. Furthermore, if the sender or receiver is a highly social node, the receiver will receive and forward the packet, mainly because social nodes help to improve the network performance [18]. We here use \(a_{1}\) to denote the forwarding action; otherwise, \(a_{2}\) is dependent on the participant status of the receiver. The type of receiver tends to be \(t_{2}\) only if the receiver/sender is a node with low sociality, i.e., when one of these nodes is not social, the receiver is not willing to participate in the data forwarding process.