## 3 Model Design
### Cooperation Probability and Energy Decomposition  
#### 3.3.1 Cooperative Probability Calculation  
(1). Node Preference  
\(Pref_{ij}\) is the degree of preference between the two nodes, \(i\) and \(j\). The node preference is different from the node encounter frequency, which refers to the time occupation ratio between two nodes establishing a connection and transmitting a message within a period of time. The specific calculation formula is as follows:  
\[Pref_{ij}=\sum\limits_{k=1}^{n}t_{i,j}^{k} \tag{13}\]  
\(t_{i,j}^{k}\) represents the total time taken for message delivery when node \(i\) and node \(j\) establish a connection for the kth time. \(t_{i,other}^{k}\) represents the total time taken for message delivery when node \(i\) and other nodes establish a connection for the kth time.  
(2). Node Relationship Stability  
\(Rel_{ij}\) is the correlation between the average interval time delivery messages of the two nodes, \(i\) and \(j\). Node relationship stability refers to the average interval between messages sent between nodes. Through it we can predict the possibility of future nodes establishing connections for a long period of time. This means that the shorter the connection interval in the most recent period, the more likely it is that the connection will be established in the future. In a period of time, the more the number of encounters, the longer the interval. Which indicates that the node has stable cooperation for a long time, as described below:  
\[Rel_{ij}=\frac{T_{i,j}^{k}-T_{i,j}^{1}}{k\times T} \tag{14}\]  
In the above equation, \(k\) is the number of message passes in \(T\) time. \(T_{i,j}^{k}\) and \(T_{i,j}^{1}\) are the time of the \(k\)th transmission of the message and time of the first transmission of the message, respectively, in \(T\) time.  
(3). Node Activeness  
We use the number of times the node forwards the message for a period of time as a measure of node activeness. The higher the node activity, the higher the degree of cooperation is to some extent. We define it as follows:  
\[Act_{i}=\frac{re_{i}}{\sum\limits_{i=1}^{n}re_{i}} \tag{15}\]  
where \(re_{i}\) indicates that the number of times the node \(i\) forwards the message is within a certain period of time, \(T\).  
(4). Data Demand  
We consider that nodes are more willing to cooperate to deliver data with common needs. At the time of message delivery, the node gives a rating feedback of the message demand. Whether a node meets and connects with other nodes within a certain period of time, the node prefers to receive and forward data useful to itself. Therefore, if the score of node feedback is higher for a period of time, it indicates that the probability that the neighbor node is willing to cooperate to forward the message is larger. Increasing this parameter can help predict the likelihood of future cooperation between nodes.  
\[Need_{ij}=\frac{\sum\limits_{\tau=1}^{k}q_{ij}^{\tau}}{Q\times k} \tag{16}\]  
where \(q_{ij}^{\tau}\) represents the data demand feedback score given by node \(j\) when node \(i\) passes a message to node \(j\). \(Q\) represents the highest score.  
Through the degree of node preference, relationship stability, activity, and data demand analysis, we can quantify the cooperation probability values between two nodes as follows:  
\[R_{ij}=aPref_{ij}+bRel_{ij}+cAct_{j}+dNeed_{ij} \tag{17}\]  
Among them, \(a,\ b,\ c,\ d\) is the coefficient of node preference, relationship stability, activity, and data demand. They respectively represent the weighting factors that influence the value of cooperation and \(a+b+c+d=1\).