# A Blockchain Network Communication Architecture Based on Information-Centric Networking
## 5 Method Analysis
### Domain Gateway Node Selection Algorithm
#### 5.2.3 Feasibility Analysis  
The domain gateway nodes elected through the local betweenness centrality evaluation protocol only play a role in accelerating broadcasting through multicast, similarly to relay network nodes. This is different from the super nodes in the consortium chain. Domain gateway nodes have no additional privileges compared to other normal nodes. Therefore, we analyzed from the perspective of game theory and concluded that this it the optimal choice for core layer nodes to serve as domain gateway nodes for both core layer nodes and edge nodes, reducing the possibility of edge nodes competing for domain gateway nodes and nodes behaving maliciously, which proves the feasibility of the algorithm. In order to analyze the benefits and costs of core layer nodes and edge nodes competing for domain gateway nodes, we designed a non-cooperative complete information static game model between core layer nodes and edge nodes:  
\[G=(\{P_{1},P_{2}\},\{S_{1},S_{2}\},\{u_{1},u_{2}\})\]  
In this model, edge nodes can also represent intermediate layer nodes, but the parameters need to be adjusted accordingly. Where \(P_{1}\) and \(P_{2}\) represent core layer nodes and edge nodes, respectively, and both types of nodes have the same two strategy sets, namely competing for domain gateway nodes and not competing for domain gateway nodes. Therefore, the strategy sets are  
\[S_{1}=\{\text{Compete},\text{Not\,Compete}\}\]  
\[S_{2}=\{\text{Compete},\text{Not\,Compete}\}\]  
\(u_{1}\) and \(u_{2}\) represent the profit functions of the core layer node and the edge node, respectively. The profit function is defined as \"profit-cost\". For the core layer node \(u_{1}\), the profit function is  
\[u_{1}= \begin{cases}R\cdot P(\alpha)(1+\delta\cdot P(c))(1+\tau(t_{1}))-C-O,& \text{if $P_{1}$ competes and $P_{2}$ competes}\\ R\cdot P(\alpha)(1-\tau(t_{2}))-C-O,&\text{if only $P_{2}$ competes}\\ R\cdot P(\alpha)(1+\delta)(1+\tau(t_{1}))-C-O,&\text{if only $P_{1}$ does not compete}\\ R\cdot P(\alpha)-C-O,&\text{if $P_{1}$ and $P_{2}$ does not compete}\\ \end{cases} \]  
For the edge node \(u_{2}\), the profit function is  
\[u_{2}= \begin{cases}R\cdot P(\alpha)(1+\delta\cdot(1-P(c)))(1-\tau(t_{2}))-C-O,& \text{if $P_{1}$ competes and $P_{2}$ competes}\\ R\cdot P(\alpha)(1+\delta)(1-\tau(t_{2}))-C-O,&\text{if only $P_{2}$ competes}\\ R\cdot P(\alpha)(1+\tau(t_{1}))-C,&\text{if only $P_{1}$ competes}\\ R\cdot P(\alpha)-C,&\text{if $P_{1}$ and $P_{2}$ does not compete}\\ \end{cases} \]  
Here, \(R\) represents the income from obtaining the right to bookkeeping, \(P(\alpha)\) is the probability function of nodes mining blocks, and \(\alpha\) is the computational power factor that represents the computational power of the node. \(C\) represents the computing cost required to mine blocks. In this game model, we assume that the income from obtaining the right to bookkeeping and the computational power are the same for both types of nodes; that is,  
\[\alpha_{1}=\alpha_{2}=\alpha,R_{1}=R_{2}=R\]  
\(\delta\) represents the profit coefficient obtained by the domain gateway node through priority block packaging after becoming a domain gateway node, \(P(c)\) represents the probability of the core node becoming a domain gateway node when both types of nodes compete for the domain gateway node, and \(1-P(c)\) represents the probability of the edge node becoming a domain gateway node. \(\tau(t)\) represents the absolute value function of the difference in message broadcast delay after becoming a domain gateway node, where \(t\) represents the broadcast delay, and \(O\) represents the additional communication and bandwidth cost required after becoming a domain gateway node. On the one hand, for the core-layer nodes, regardless of whether they become domain gateway nodes or not, they need to incur the same cost of bandwidth and communication expenses \(O\).