## 3 Collaborative Monitoring Algorithms for Situational Assessment
### Collaborative Traffic Trend Prediction Approach
#### 3.2.2 Monitoring Indicator Weight Calculation  
Game theory is an essential sub-discipline of operations research, which mainly studies the interaction between competing things and analyzes the rational behavior of multiple decision makers and their decision equilibrium when they interact with each other. This requires the parties to find an equilibrium combination that maximizes their common interests, i.e., requires the combination of weights and the minimization of the deviation between the weights [37; 38], and the larger deviation produces a \"compromise\". The game theory-based portfolio assignment method takes the Nash equilibrium as the goal, coordinates the conflict between subjective and objective weights and finds the agreement and compromise between them, which is an integrated process of mutual comparison and mutual coordination. The method can reduce the subjective arbitrariness and also fully consider the influence of objective data to a certain extent to improve the scientific rationality of the assignment. The AHP and EM combination weight calculation method based on Game Theory (GT-AHP-EM) uses two assignment methods to calculate the weights and then performs a secondary weighting to obtain the final weights. The AHP method was used for the subjective assignment part, and the EM method was used for the objective assignment. The Analytic Hierarchy Process (AHP) is a multi-program decision-making method proposed by Professor [PERSON], an American operations researcher. It can solve complex decision problems with multiple objectives, criteria, elements and levels. The method [39] decomposes the decision problem into numerous levels of objectives, criteria and scenarios for evaluating decisions and quantifies and correlates the relevant elements. Usually, two and two influence factors are compared [40], and the judgment matrix is constructed using the 1-9 scale method to synthesize the weight of the intrinsic influence between factors. The entropy method (EM) is a mathematical method that can calculate the dispersion of indicators. It derives indicator weights from the amount of information provided by the indicator. If the influence of the indicator on the evaluation results is more substantial, it means that the variability among the indicators is greater. Therefore, the weights can be calculated according to the variability in indicators to provide theoretical support for comprehensive evaluation. In this paper, the GT-AHP-EM method can not only consider the inherent information among indicators, but also reduce the one-sidedness of the single assignment method. This method improves the rationality of indicator assignment in the following steps [41]. Step 1: Calculation of weights using the AHP method. The construction of judgment matrix \(B=\left[ \begin{array}{ccc}b_{11}&\cdots&b_{1M}\\ \vdots&\ddots&\vdots\\ b_{M1}&\cdots&b_{MM}\end{array} \right]\) is carried out according to the indicator set \(U\), where \(b_{ij}\) shows the importance of the \(i\)th indicator relative to the \(j\)th indicator in the indicator set \(U\). Then, we determine the maximum eigenvalue \(\lambda_{\text{max}}\) and the normalized eigenvector \(W_{1}\) of the judgment matrix \(B\). In this paper, the arithmetic average method is used to calculate the maximum eigenvalues of the judgment matrix and its corresponding eigenvectors. The calculation of this method is shown in Equations (19) and (20). \[w_{1i}=\frac{1}{M}\sum_{j=1}^{M}\frac{b_{ij}}{\sum_{k=1}^{M}b_{kj}},(i=1,2, \ldots,M) \tag{19}\]  
\[\lambda_{\text{max}}=\sum_{i=1}^{M}\frac{(Bw)_{i}}{Mw_{1i}} \tag{20}\]  
The Consistency Ratio \((CR)\) is used as a comprehensive indicator to ensure average randomness and consistency. If \(CR<0.1\), the consistency of judgment-matrix is well; if \(CR>0.1\), the judgment matrix should be reconstructed. The consistency test is calculated as shown in Equations (21) and (22).