# The Evolution of Service Ecosystems Based on the Lotka-Volterra Model
## 4 Results
### Design of Service Proxy Nodes
#### 4.2.2 Service Proxy Node Mobility Strategy  
In terms of mobile decision design for service proxy nodes, this paper uses a more realistic environment based adversarial game approach. From a realistic comparison perspective, this paper maps the relevant decisions made by service providers in the real world into an adversarial game, where the two parties in the adversarial game correspond to market regulators and service providers respectively. The purpose of market regulator regulation is to maximize the total profits in the local market, while the service provider decision-making is to maximize their own profits. Both parties continuously coordinate and communicate until a solution that is satisfactory to both each other. The detailed flowchart is shown in Figure 3.  
In the computational experimental system, adversarial games are manifested in the mobility strategy of service agent nodes. Service agent nodes consider changing their own node decisions under the influence of market regulators to maximize the current individual node's profits, while market regulators consider changing the mobility decisions of all \begin{table}
\begin{tabular}{c p{142.3 pt}} \hline \hline
**Key Attributes of Service Proxy Nodes** & **Explanation of Attributes** \\ \hline Service type & Determine which type of service the service proxy node provides \\ Asset value & Calculated based on the cumulative difference between the profit and \\ Service scale scope & Deciding how large a service proxy node can provide \\ Mobile speed & It determines the movement speed of service proxy nodes in the \\  & experimental environment. The faster the movement speed, the faster it \\  & can seize the demand in the environment and gain profits \\  & It determines the viewing radius of the service proxy node in the map. \\ Range of field of view & The larger the field of view radius, the easier it is to observe more demands \\  & in the environment \\ Lifecycle state & Depending on the behavior of the current service proxy node, it has four \\  & states: survival, extinction, evolution, and fragmentation \\ Service proxy node name id & The service proxy node represents the services and service providers in the framework \\ \hline \hline \end{tabular}
\end{table} 
Table 2: An explanation of service proxy node properties in computational experimental system. service agent nodes within a certain area to maximize the total market revenue within the area. Based on the decisions made by the other party, both parties continuously adjust the game to seek a consistent strategy combination, that is, to achieve equilibrium in the game, and ultimately determine the decision-making behavior of the service agent node.The expression for maximizing the benefits of both parties in the game is shown in Equation (26):  
\[\left\{ \begin{aligned} &\underset{S_{i}}{argmax}\Big{(}V_{single}(S_{i},S_{-i}) \Big{)}=DecisionCombination\Big{(}S_{1}^{1},S_{2}^{1},\ldots,S_{n}^{1}\Big{)}\\ &\underset{S_{-i}}{argmax}\big{(}V_{region}(S_{-i},S_{i})\big{)}= DecisionCombination\Big{(}S_{1}^{2},S_{2}^{2},\ldots,S_{n}^{2}\Big{)}\end{aligned} \right. \tag{26}\]  
where \(V_{single}\) represents the profit calculation function of the service proxy node; \(V_{region}\) represents the profit calculation function for all service agent nodes in the regional market; The parameter \(a\) in \(V(a,b)\) represents the service proxy node that needs to be adjusted to achieve maximum revenue, while the parameter b represents the fixed service proxy node; \(S_{i}\) represents the \(i\)-th service proxy node; \(S_{-i}\) represents service proxy nodes other than the i-th node; \(S_{i}^{j}\) represents the mobile decision made by the \(i\)-th service proxy node to maximize the interests of party \(j\); \(DecisionCombination\) represents combining the strategies optimized respectively by the service agent nodes and the market regulators into a final decision set. To some extent, adversarial game decision making is a method for achieving optimal solutions.