Please answer in a,b,c,d,e separately. Thanks.

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4. Three board members are going to vote for a president from them: Ava, Bob and Chloe. Each member is both a candidate and a voter. Here is the voting rule: each member votes for one candidate (voting for oneself is allowed); if two or more people vote for the same candidate then that person is chosen as the president; if there is exactly one vote for each candidate, then the person for whom Ava voted is selected as the president. (a) Represent this voting procedure as a game frame, indicating inside each cell of each table which candidate is elected, i.e., using the president's name as the payoff value. [6 Marks] (b) Convert the game frame into a 3-person non-zero-sum game with the following payoff values: The president payoff values for Ava: Ava - 2, Bob -0. Chloe - 1. The president payoff values for Bob: Ava - 1, Bob - 2, Chloe - 0. The president payoff values for Chloe: Ava - 0, Bob - 1, Chloe - 2. [6 Marks] (c) Find the Nash equilibrium of this game. Explain your reason clearly. [6 Marks] (d) Find the Pareto optimality of this game. Explain your reason clearly. [6 Marks) (e) Does the extra power given to Ava (in case of one vote for each candidate) benefit Ava? 4. Three board members are going to vote for a president from them: Ava, Bob and Chloe. Each member is both a candidate and a voter. Here is the voting rule: each member votes for one candidate (voting for oneself is allowed); if two or more people vote for the same candidate then that person is chosen as the president; if there is exactly one vote for each candidate, then the person for whom Ava voted is selected as the president. (a) Represent this voting procedure as a game frame, indicating inside each cell of each table which candidate is elected, i.e., using the president's name as the payoff value. [6 Marks] (b) Convert the game frame into a 3-person non-zero-sum game with the following payoff values: The president payoff values for Ava: Ava - 2, Bob -0. Chloe - 1. The president payoff values for Bob: Ava - 1, Bob - 2, Chloe - 0. The president payoff values for Chloe: Ava - 0, Bob - 1, Chloe - 2. [6 Marks] (c) Find the Nash equilibrium of this game. Explain your reason clearly. [6 Marks] (d) Find the Pareto optimality of this game. Explain your reason clearly. [6 Marks) (e) Does the extra power given to Ava (in case of one vote for each candidate) benefit Ava