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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 di erent 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 payo s of each candidate in each case.
(c) Interpret the results (important).
Based on the following graphs (next page) you should write a discussion report (2 pages) on: 1. Determination of whether the open-loop system response is consistent with a 1st o
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