Consider a simultaneous move game between two players given by the following matrix: L R T $2,11,1$ M $1,01,1$ B $0,01,2($a$)(25$ points$)$ Find all the Nash equilibria in mixed strategies. $2.$ Consider the following policy game. The house of representatives $($player $1)$ can propose a new federal minimum wage of x in $[10,20].$ After player $1$ proposes x$,$ the senate $($player $2)$ observes the proposal and decides whether to accept or reject it$.$ If proposal x is accepted then payoffs are u$1($x$)=5+$x for player $1$ and u$2($x$)=20$x for player $2.$ If player $2$ rejects the proposal then both players get a payoff of $7\mathrm{.}25.($a$)(10$ points$)$ Draw the game tree. How many subgames does it have? Give an example of a strategy of each player. $($b$)(20$ points$)$ Find a subgame perfect equilibrium of this game. Is it unique? $($c$)(10$ points$)$ Find a Nash equilibrium that is not subgame perfect. $3.$ Two team members can invest time and effort in creating a better working relationship. Each invests ei in $[0,2],$ and if both invest more then both are better off, but it is costly for each team member to invest. In particular, the payoff function for player i is ui$($ei $,$ e$$i$)=(1+$ e$$i$)$ei $$e $2$ i $.$ The team leader, player $1,$ chooses her effort level e$1$ first. Player $2$ observes e$1$ and then chooses his own effort level e$2.($a$)(25$ points$)$ Find the subgame perfect Nash equilibrium. $($b$)(10$ points$)$ Does the team leader enjoy a first mover advantage?