Bayesian Game Based Decision-making
Since the core algorithm for the interaction is the decision-making process, and the aggressiveness Observation & update module is designed to serve this process, we move the decision-making algorithm section forward though it is at the middle part of the proposed framework. This module is based on the Bayesian game theory which makes no assumptions on the accessibility of the cost function of the opponent or leader of the game. However, in order to simulate the subject for different scenes, cost function of the Player One is still required, which will be further formulated in the rest of this section.
Numerous scholars have studied game-theoretic approaches,in which an N-player game for \(N = 2,3,...,n\) can be simplified into a two-player game, i.e., \(N = 2\) . For each player \(i\in N\), he or she has at least two alternative solutions based on the problem definition represented by a discrete set of \(A_i=\left\{a_{i,1},a_{i,2},\dots,a_{i,k},\dots,a_{i,K}\right\}, K\in\left[2,\infty\right]\)and the utility function given by \(u_i(a_{i,k},a_{i^{\prime},k^{\prime}})\). Based on the conflicts definition, \(A_i\) comprises two clusters of strategies, i.e. \( A_i = \left\{A_{i,F}, A_{i,Y}\right\}\). \( a_{i,F}(a_{i,F}\in A_{i,F})\), is the optimal or expected trajectory that maximize or minimize the utility function among all the alternatives to fight. And the mechanism is the same for the yielding type \(a_{i,Y}\in A_{i,Y}\). Without loss of generality, the best solution always dominates the rest choices, thus it is not necessary to list all the choices.