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. $A_i = \{A_{i,F}, A_{i,Y}\}$. $a_{i,F}(a_{i,F}\in A_{i,F})$, 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.