1. Majority Voting (Exercise 1.2* in Fudenberg and Tirole). There are three players, 1, 2, and 3, and three alternatives {A, B, C}. Each player votes for an alternative; the alternative with the most votes wins. If there is no majority for any alternative, the alternative A wins. Player 1 ranks the alternatives as follows: AmBC. For players 2 and 3 we have B > 20 >2 A and C > 3A >3 B, respectively. (a) Write this situation as a game in normal form. That is, define (i) the individual strategy sets and (ii) the individual utility functions over strategy profiles so that the players' preferences over alternatives are represented. (Hint: Denote by (a, b, c) the strategy profile according to which player 1 votes for A, player 2 for B, etc. Abbreviate, e.g., by the expression #a E s = 1 the statement that exactly one player has voted for alternative A given the strategy profile s.) (b) How many strategy profiles are there? (c) Derive the individual best response correspondences. (d) Identify all Nash equilibria. (Hint: Use the brute force method, that is, write down all strategy profiles and check if some player has an incentive to deviate.) (e) Is there some Nash equilibrium that seems to be more plausible than the others? (Argue)