9.3 Campaigning Revisited: Two political candidates are scheduled to campaign in two states, in one in period t = l and in the other in t = 2. In each state each candidate can choose either a positive campaign that promotes his own agenda (P for player 1. p for player 2) or a negative one that attacks his opponent (N for player 1, n for player 2). Residents of the rst-period state do not mind negative campaigns, which are generally effective, and payoffs in this state are given by the following matrix: Player 2 Player I In the second-period state, residents dislike negative campaigns despite their effectiveness, and the payoffs are given by the following matrix: Player 2 Player 1 a. What are the Nash equilibria of each stage-game? Find all the pure- strategy subgame-perfect equilibria with extreme discounting (6 = 0). Be precise in dening history-contingent strategies for both players. b. Now let 5 = 1. Find a subgame-perfect equilibrium for the two-stage game in which the players choose (P, p) in the rst stage-game. c. What is the lowest value of 6 for which the subgame-perfect equilib- rium you found in (b) survives? (1. Can you nd a subgame-perfect equilibrium for this game in which the players play something other than (P, p) or (N, n) in the rst stage