Exercise 1.12. Consider the following game. There is a club with three members: Ann, Bob and Carla. They have to choose which of the three is going to be president next year. Currently Ann is the president. Each member is both a candidate and a voter. Voting is as follows: 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 next president; if there is complete disagreement, in the sense that there is exactly one vote for each candidate, then the person from whom Ann voted is selected as the next president. (@) Represent this voting procedure as a game frame, indicating inside each cell of each table which candidate is elected. (b) Assume that the players' preferences are as follows: Ann >, Carla >, Bob, Carla >,, Bob>,, Ann, Bob-. K Ann>. Carla. Using utility values 0, 1 and 2, convert the game frame into a game. (c) Apply the IDWDS to the game of part (b). Is there a weak iterated dominant- strategy equilibrium? (d) Does the extra power given to Ann (in the form of tie-breaking in case of complete disagreement) benefit Ann