4. Two players, P1 and P2, are bargaining over sharing $10. The bargaining lasts 3 periods. They are making alternating offers. The time discounting factors are given by 1 = 1 4 and 2 = 1 2 . 1In period 1, P1 makes an offer of x2 where x2 10 and P2 either accepts or rejects it. If P2 accepts, then the game ends, and they receive (u1, u2) = (10 x2, x2). If P2 rejects, the bargaining moves on to period 2. In period 2, the roles are reversed. Now P2 makes an offer x1 where x1 10 and P1 either accepts or rejects it. If P1 accepts, then the game ends, and they receive (u1, u2) = (x1, 10 x1). If P1 rejects, then the bargaining moves on to period 3. In period 3, the bargaining is basically the same as the one in Period 1, except that if P2 rejects P1's offer, both receives zero. (This is an ultimatum game.) (1) Write down the SPE of the subgame in period 3. (2) Write down all P2's offers in period 2 that would be accepted by P1 under the SPE. And write down P2's offer. (3) Write down all P1's offers in period 1 that would be accepted by P2 under the SPE. And write down P1's offer. Write down the payoffs received by P1 and P2 under the SPE.