## 4 Social Mechanism
### Economic Incentive Value  
Incentive mechanisms have been extensively employed in blockchain data-sharing schemes to enhance data reliability. In DC-SoC, economic interest value exhibits two distinct differences compared to trust value. Firstly, unlike the passive evaluation of peers in trust value, economic interest value assumes an \"active\" role for peers. This arises because each user, functioning as an independent economic entity, possesses self-interested attributes within the social network. By distributing benefits, the incentive mechanism motivates participants to enhance service quality and data reliability, leading to increased profits [27] and fostering a positive cycle of data sharing. Secondly, the economic benefits value emphasizes the degree of data authenticity rather than the stability of peers. For instance, in the coalition chain system, if a peer propagates distorted data, this behavior is quantified as a penalty value that is incorporated into the economic value calculation for that particular peer. To comprehend the specific calculation of the economic benefits value, it is essential to introduce the definition of the combined trust value in (4):  
\[CT_{b}=\frac{\sum_{i\in N}T_{ib}}{n} \tag{4}\]  
\(N\) represents the set of neighboring peers of peer \(b\), including peers with which it has had interactions, and \(n\) denotes the number of peers in set \(N\). \(CT_{b}\) refers to the combined trust value of peer \(b\), which is calculated as the average of the sum of trust values between peer \(b\) and all its interacting peers. Afterward, DC-SoC defines the value of economic interest for a peer using (5):  
\[E_{B_{b}}= \begin{cases}\frac{F}{\sum_{i\in N}CT_{i}}\cdot CT_{b}&CT_{b}>0\\ 0&CT_{b}\leq 0\end{cases}  \tag{5}\]  
\(EB_{b}\) denotes the value of the economic benefit associated with peer \(b\). \(F\) is an initial benefit coefficient set to 1. As peer \(b\) disseminates increasingly distorted data in the network, \(F\) gradually converges to 0. Conversely, if peer \(b\) maintains honesty, \(F\) grows and ultimately converges to a constant value \(m\). The specific value of \(m\) depends on the application. The variation of \(F\), as determined by the curve, is typically described using sigmoid or arctan functional expressions. In summary, economic interest differs from trust value as it is a global variable. Regardless of the current transaction's counterpart, the economic interest of the peer remains constant and is updated in real-time based on the transaction. Once the trust value and economic benefit value have been derived, the final socialization value can be calculated using (6):  
\[SV_{ab}=EB_{b}*T_{ab} \tag{6}\]  
\(SV_{ab}\) represents the social value resulting from the interaction between peer \(a\) and peer \(b\). \(S\) consists of peer \(a\)'s neighboring peers and the peers it has interacted with. Finally, by normalizing \(SVab\), it can be transformed into the transaction probability between peer and peer \(b\), which represents the likelihood of peer \(a\) accepting a transaction request from peer \(b\). The algorithm dynamically adjusts both a node's local and global trustworthiness based on its historical behavior and current performance. Local trustworthiness is derived from interactions with neighboring nodes, primarily considering the number of successful data transmissions, data accuracy, and response times. The more frequently a node interacts with highly trustworthy nodes while consistently providing reliable data, the higher its local trustworthiness becomes. In contrast, global trustworthiness is evaluated through cross-cluster interactions, where the success rate and stability of a node's data propagation across different clusters determine its global influence. Nodes demonstrating consistent performance gain higher global trustworthiness. Moreover, economic incentives are used to reward nodes that contribute to network security and propagation efficiency, which in turn enhances their social credibility.