We now revisit the electoral competition game. Assume there are now 3 candidates, and that if a group of two or three of the candidates choose the same position, they will split the voters closest to them equally between them. We also change the payoff functions: instead of awarding 1 to the winner and 0 to the losers, assume that each candidate's payoff is equal to the fraction of voters voting for them. Does this game have Nash equilibria (in pure strategies)?

Microeconomics: Principles & Policy
14th Edition
ISBN:9781337794992
Author:William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:William J. Baumol, Alan S. Blinder, John L. Solow
Chapter13: Between Competition And Monopoly
Section: Chapter Questions
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be detailed. please Show the profitable deviations in each case for some player

3. We now revisit the electoral competition game. Assume there are now 3
candidates, and that if a group of two or three of the candidates choose the
same position, they will split the voters closest to them equally between them.
We also change the payoff functions: instead of awarding 1 to the winner and
0 to the losers, assume that each candidate's payoff is equal to the fraction of
voters voting for them.
Does this game have Nash equilibria (in pure strategies)?
Transcribed Image Text:3. We now revisit the electoral competition game. Assume there are now 3 candidates, and that if a group of two or three of the candidates choose the same position, they will split the voters closest to them equally between them. We also change the payoff functions: instead of awarding 1 to the winner and 0 to the losers, assume that each candidate's payoff is equal to the fraction of voters voting for them. Does this game have Nash equilibria (in pure strategies)?
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