I am stuck on this part of my homework\

Part 3: A Board Game Arturo and Beatrice are playing the board game "Colonizers of Katan Legacy." There are two turns left in this game, with Arturo and Beatrice currently tied at 12 points each. It is Arturo's turn. Arturo can decide to pass, which ends this game in a tie, or move the game to the final round. If the game reaches the final round, each player decides simultaneously to either go to war or call for peace. If both players call for peace, they get one extra point each. If both players call for war, they get minus 10 extra points each. If one calls for peace and the other calls for war, the person who calls for war gets 4 extra points, and the other person gets minus 4 extra points. Players want to maximize their total individual points in the game. That is, a player's payoff is the sum of her current points and whatever points she gets in the final round, if a final round takes place. 10. Consider the subgame that starts if Arturo moves the game to the final round. What are the pure and mixed strategy Nash equilibria of that subgame? (a) Pure strategy equilibria: (War, Peace); (Peace, War) Mixed strategy equilibrium: Arturo plays "War" with probability ; and "Peace" with probability -, and Beatrice plays "War" with probability } and "Peace" with probability . (b) Pure strategy equilibria: None Mixed strategy equilibrium: Arturo plays "War" with probability } and "Peace" with probability , and Beatrice plays "War" with probability } and "Peace" with probability 1. (c) Pure strategy equilibria: (War, Peace); (Peace, War) Mixed strategy equilibrium: Arturo plays "War" with probability ; and "Peace" with probability ,, and Beatrice plays "War" with probability } and "Peace" with probability ]. (d) Pure strategy equilibrium: (War, War) Mixed strategy equilibrium: Arturo plays "War" with probability } and "Peace" with probability , and Beatrice plays "War" with probability , and "Peace" with probability . 11. What is the expected payoff for each player under the mixed strategy Nash equilibrium in the final round subgame? (a) 22.66 6 (b) 11.33 (c) 12 (d) 13 12. Now consider the whole game. Focusing exclusively on the Subgame Perfect Nash Equilibrium in which a mixed strategy is played in the final round subgame, what can we say about Arturo's equilibrium decision of whether to pass or take the game to the final round? (a) Arturo passes (b) Arturo moves the game to the final round (c) Arturo plays a mixed strategy, in which both passing and moving the game to the final round can happen with positive probability (d) We do not have enough information to answer this