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 dierent platforms the challenger wins the election.

- The payo for winning the election is 2 and the payo 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 payo 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 rst

(a-2) The Challenger moves rst

(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 payos of each candidate in each case.

(c) Interpret the results (important).