Problem $2.[5$ points$]$ Monte Carlo Tree Search $($MCTS$)$ for target tracking. Consider a target tracking problem where two robots must jointly track one target. Each robot i in $\{1,2\}$ has two actions $\{$a $1$ i $,$ a$2$ i $\}.$ The target also has two actions $\{$b $1,$ b$2\}.$ The robots use EKF to estimate the position of the target and they want to minimize the uncertainty of the target$$s position at a future time step T$,$ quantified by the trace of the target$$s covariance matrix, i$.$e$.,$ trace$($T $).$ In contrast, the target wants to maximize this uncertainty. Write down the steps of using MCTS and draw the decision tree to solve this problem. Feel free to use any notations you need. $($Hint: Section $3\mathrm{.}2.)$