2. (20 points) A public facility needs to be located on a street of length 1, denoted by the interval [0, 1]. In the city there are n voters. Each voter i has an ideal location pi E [0, 1], where she wants the facility to be located. If the facility is located at location l E [0, 1], then her payoff is - (Pi - 1 ) 2.The following voting game is played to decide on the location. Every citizen i votes for a location xi E [0, 1]. The vote profile is x = (Xi, . . . , Un). Then the facility is chosen at the location W(x) where W(x) we will call the voting rule. The specific voting rule that the city uses is W (x ) = min {x1, . . . , an). (a) Define the game in Normal form (3 points) (b) Is it a dominant strategy (weakly) for each voter , to vote for her ideal location ? (7 points) (c) If instead the city used the voting rule V (x) = max{ x1, . . . , In) would your answer to part (b) change? Why or why not ? (5 points) im (d) The city uses the voting rule U (20 ) = min { *1 , . . . , n) + max { 21 , . . . , In) 2 Now is there a change in your answer to part (b). Explain? (5 points)