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. (a) 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 Ann Carla Ann Bob, Carla Bob Bob Bob Ann, Bob Carla Ann Carla 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?