8 Us backward induction to solve the decision tree below.Player 1UpOUp)O (Up, Down)(Down, Up)(Down, Down)DownPlayer 2Player 2UPDownUPDown$200 for Player 1; $300 for Player 2$100 for Player 1; $200 for Player 2$200 for Player 1; $100 for Player 2$300 for Player 1; $200 for Player 2What is the Subgame Perfect Equilibrium (SPE) of this game? [SPE]10

We solve all the sequential games using backward induction. This means we first solve the moves made by last player and on tge basis of that move to the first.All sequential games are solved backwards. So we solve game 1 marked in the above picture. Player 2 has two options up and down. Up gives him a payoff of $200 and down gives him a payoff of $100. So to maximize utility player 2 will choose up and get $200. Hence, that payoff moves backward and we write $200. Now, coming to game 2 Player 2 has two options again which are up and down which gives him a payoff of $200 and $300 respectively. Obviously player 2 chooses $300 which is down. So now that move backwards and we write the payoff. Finally we solve game 3. Now we have the payoffs for player 1 which is $200 for up and $300 for down. So again to maximize the payoff player 1 should down and get the payoff of $300. Hence, the sub perfect Nash Equilibrium becomes (Down,Down). Player 2 chooses down (in game 2) and then on the basis of that player 1 chooses down (in game 3). The last option (Down, Down) is the correct option.