PROBLEM (3) (Ultimatum Game) The proposer proposes an allocation (x,y) where he gets $x himself and leaves $y = 10-x for the responder. find all the pure sequentially rational Nash Equilibria (if any) assuming the players have the following utility functions over the final money allocation: a) u1 (x, y) = Vx+ vy = uz(x,y) b) uj (x, y) = Vx - 0.5vy, uz(x, y) = y - 0.5vx c) ul (x, y) = xty= uz(x,y) d) u1(x, y) = 2x + y, u2(x, y) = 2y+ x