Problem 1: An election is being held in which there are two candidates, A and B. There are five voters: 1, 2, 3, 4 and 5. The preferred candidate for players 1, 2 and 3 is A and the preferred candidate for voters 4 and 5 is B. Voters must vote either for candidate A or for Candidate B and they care only about whether their preferred candidate wins (the best outcome), or loses (the worst outcome), and not about the margin of victory or loss. A tie is not possible, since the number of voters is odd.
Part A : In the following matrices construct payoff functions for the representative voter who prefers candidate A and one who prefers candidate B. In both, VA is the number of voters, other than the representative voter, who vote for candidate A. Indicate the best responses by underlining payoffs.
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Prefers A VA =0 VA = 1 VA= 2 VA= 3 VA= 4
A
B
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Prefers B
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VA= 0
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VA= 1
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VA= 2
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VA= 3
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VA= 4
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A
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B
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Part B : Describe all of the Nash equilibria of the game.
Part C : Which equilibrium do you think is the most likely? Why?