Question 3 (Iterated Elimination of Dominated Strategies 30 points) A three-person committee has to choose a winner for a national art prize. After some debate, there are three candidates still under consideration: a woman who draws an- telope in urban settings, a man who makes rectangular lead boxes, and a woman who sculpts charcoal. Let's call these candidates a, b and c; and call the committee members 1,2 and 3. The preferences of the committee members are as follows: member 1 prefers a to b and b to c member 2 prefers c to a and a to b; and member 3 prefers b to c and c to a. The rules of the competition say that, if the committee members disagree, they should vote (secret ballot, one member one vote) and that, if the vote is tied, the winner will be the candidate for whom member 1 voted. (a) Consider this voting game. Each voter has three strategies: a, b, or c. For each voter, which strategies are weakly or strictly dominated? (Hint: To answer this question, you do not need to know the exact payoffs; any payoffs will do provided that they are consistent with the preference orders given above. For ex- ample, assign payoff of 3 to a voter's top choice, 2 to second choice, and 1 to third choice.) (b) Now consider the reduced game in which all weakly and strictly dominated strate- gies have been removed. For each voter, which strategies are now weakly or strictly dominated? (c) Is this game dominance-solvable? What are the Nash equilibria of the game? Are they also Nash equilibria in dominant strategies? (d) What is the predicted outcome of the vote? Compare this outcome to voter l's preferences and comment