(Voting) Find all the Nash equilibria of the game. (First consider action profiles in which the…
(Voting) Find all the Nash equilibria of the game. (First consider action profiles in which the winner obtains one more vote than the loser and at least one citizen who votes for the winner prefers the loser to the winner, then profiles in which the winner obtains one more vote than the loser and all citizens who vote for the winner prefer the winner to the loser, and finally profiles in which the winner obtains three or more votes more than the loser.) Is there any equilibrium in which no player uses a weakly dominated action? Consider a variant of the game in which the number of candidates is greater than two. A variant of the argument above shows that a citizen’s action of voting for her least preferred candidate is weakly dominated by all her other actions. The next exercise asks you to show that no other action is weakly dominated.
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