A rightist incumbent (player I) and a leftist challenger (player C) run for senate. Each candidate chooses among two possible political platforms: Left or Right. The rules of the game are the following: - If both choose the same platform, the incumbent wins the election and if they choose different platforms the challenger wins the election. - The payoff for winning the election is 2 and the payoff of losing is 0 for each candidate. - Moreover, candidates do not like to compromise their views. Therefore, independently of whether they win or not, they get an extra payoff of 1 (that is, on top of the 0 or 2 mentioned above) if they propose the platform they like best. (a) Draw the tree if: (a-1) The Incumbent moves first (a-2) The Challenger moves first (a-3) The Incumbent and the Challenger move simultaneously (b) Find the Backward induction equilibrium in cases (a-1) and (a-2) and the (pure and/or mixed strategy) Nash equilibria in case (a-3). Find the payoffs of each candidate in each case. (c) Interpret the results (important)