1. Two political candidates are racing in two states, in one in period t = 1, and in the other in t = 2. In each state each candidate can choose either a positive campaign that promotes her own agenda (P for player 1 and p for player 2) or a negative one that attacks her opponent (N for player 1 and n for player 2). Residents of the first state do not mind the negative campaigns and the payoffs in this state are as follows: P N P 2, 2 0,5 N 5.0 3, 3 In the second state, residents dislike negative campaigns and the payoffs are given by: P N P 4, 4 1, 0 N 0, 1 2, 2 (a) What are the Nash equilibria of each stage game? (b) Let 6 = 1. Find the subgame perfect equilibrium for the two-stage game in which the players choose (P, p) in the first stage. Be precise in defining history-contingent strategies for both players. (c) What is the lowest value of 6 for which the SPNE that you found in the previous period survives? (d) Can you find a SPNE in which the players play something other than (P, p) or (N, n) in the first stage