Consider the following game: (7,3) and P1 (4,5) b (3,6) Suppose each player has Fehr-Schmidt preferences. So, for an outcome (1, 2), we have U(1, ) = 21-a max{2x,0} - 3 max{x2,0} P2 U(1,2)=x2-a2 max{1x2,0} - 3 max{2x1,0} Throughout this problem, assume 32 > 1/1. (a) Compute U(4, 5) and U(3, 6). Which action will P2 choose at their decision node? (b) Compute U(7,3) and U(4, 5). Under what condition will P1 prefer outcome (4,5) over (7,3)? (The condition is an inequality involving a and 3). (c) The Fehr-Schmidt model assumes 0 3 < 1 and a; 23; for each player i. Under these assumptions, will P1 prefer (4,5) over (7,3)? (d) Suppose we drop the requirement that a; 23. In particular, let a = and 3 = 1/2 Find the subgame perfect Nash equilibrium of the game, and provide some intuition for the result (a few sentences should suffice).