Please help me with the following questions on Game Theory

4. HOTELLING'S MODEL (15PTs) Consider the HotellingDowns electoral competition model with four players, each chooses a policy position on the real line to maximize their probability of winning the election. Now assume that the voters' ideal policies are distributed uniformly over [0, 1]. (This means that, for all 0 S a, g b g 1, the proportion of the voters with ideal policies between a; and b is equal to b 0,. Thus, the median voter now has ideal policy .) (1) Now consider the action prole (i, %, g, g), i.e., players 1 and 2 choose %, while players 3 and 4 choose policy platform g. Is this action prole a Nash equilibrium? Explain your answer. [5 pts) (3) Now suppose that there are still three players but the players' objective is to maxi 122 mize their vote share (the proportion of voters voting for them). Is g, g, 5) a Nash equilibrium? Explain. (5pts) (2) Now suppose that there are only three players. Is (, 2, 2) a Nash equilibrium? Explain. (5pts)