5. Tie breaker. Three economics professors A, B, and C comprise the hiring committee for a new assistant (25) professor. Professor C is the chair of the committee. They have narrowed the candidates to the top three: X, Y, and Z. Preferences are as follows. You may assume that the getting your most preferred outcome gives a utility of 3, second best gives 2, and least preferred gives 1. A : X ? Y ? Z B : Y ? Z ? X C : Z ? X ? Y The voting proceeds in order with A and B voting first, and then the chair; everyone observes the previous votes. However, along the lines of the U.S. Senate, the chair votes only if there is a tie between the other two voting members. And, in that case, must choose only between the tied candidates; i.e., if A votes for X and B votes for Y, then C casts the deciding vote between X and Y. (a) Draw the extensive form of the game where A votes first and then B votes; all votes are observed in order. C votes if there is a tie. (b) What is the subgame perfect equilibrium of the game in (a)? What is the equilibrium path? Who gets their preferred candidate? (c) Now suppose that B votes before A (again, with all votes observed by everyone). C votes if there is a tie. What is the subgame perfect equilibrium of the game? [You do not need to draw the extensive form, but you may if it helps you to justify your answer.] (d) Now suppose that A and B vote simultaneously (or in a secret ballot). Draw the strategic form of the game between A and B, where you have already solved for C's strategy. What is the subgame perfect equilibrium? What is the equilibrium path? Who gets their preferred outcome? (e) Would you say there is a first mover advantage in this game? Explain in a paragraph or two

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