EXERCISE 47.1 (Voting) Find all the Nash equilibria of the game. (First consider

Question

EXERCISE 47.1 (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?

Explanation / Answer

In Case 1:-

Here we will consider that the winner receives one more vote than the loser and at least one citizen who votes for the winner is preferring the loser over the winner and any citizen who votes for the winner and prefers loser over the winner can by changing his vote cause his favorite contestant to win rather than lose. But here no such action profile is a Nash equilibrium.

In Case 2:-

Here we will consider the situation given in the question. For simplicity, we will denote A and B as two contestants. Here as per the question majority of the citizens wants A over B and so the winner has to be A.No citizen who prefers A over B can make a better outcome by changing her vote as her favorite candidate is going to win. But is anyone is prefering B over A and every such citizen is voting for B, any change in their vote has no effect on the outcome because A still wins. Thus here action profile is Nash equilibrium.

Case 3:-

Here we will consider that an action profile in which the winner has received at least 3 more votes than the loser. In such case, any change in any citizen vote has any effect on the outcome. Every action is Nash equilibrium.

The one and only equilibrium in which no player uses a weakly dominated action is when they vote for their favorite contestant.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.