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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).
Mathematical Properties The sum of deviations of the items from the arithmetic mean (taking signs into account) is always zero, i.e. = 0. The sum of
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