In: Economics
Consider the following game. There are 10 political positions, 1, · · · , 10, from the most liberal to the most conservatives. Two politicians simultaneously choose what position they pick in order to maximize the percentage of votes they can get. 10% of voters are at each position. Voters will vote for the politician they are closer to. If two politicians choose the same position then they each get 50% of the votes.
(a) Solve this game by iterative deletion of strictly dominated strategies.
(b) What are (pure-strategy) Nash equilibria of this game?