5. Consider a game where two voters decide on who to elect to a given office between two candidates. The economy can be in two states that we will call A and B; both voters agree that candidate 1 is the best if the state is A but candidate 2 is more suitable if the state is B. Assume that both voters' preferences are represented by the Bernouilli utility function that gives payoff 1 if the right candidate is elected for the realized state and 0 otherwise; if the candidates tie, each is selected with probability 1/2 so that expected payoff then is 1/2. Voter 1 is informed of the state of the economy while voter 2 is not. Voter 2 believes that the state is A with probability .9. Each voter has the option to vote for candidate 1, for candidate 2, or to not vote. (a) Formulate this situation as a Bayesian game. (b) Show that the game has exactly two pure strategy bayesian Nash equilibria, in one of which voter 2 does not vote and in the other of which they always vote for candidate 1. (c) Show that the action of one of the players in the second equilibrium is weakly dominated. (d) Why is "swing voter's curse" an appropriate name for the determinant of voter 2 in the first equilibrium ?

5. Consider a game where two voters decide on who to elect to a given office between two candidates. The economy can be in two states that we will call A and B; both voters agree that candidate 1 is the best if the state is A but candidate 2 is more suitable if the state is B. Assume that both voters' preferences are represented by the Bernouilli utility function that gives payoff 1 if the right candidate is elected for the realized state and 0 otherwise; if the candidates tie, each is selected with probability 1/2 so that expected payoff then is 1/2. Voter 1 is informed of the state of the economy while voter 2 is not. Voter 2 believes that the state is A with probability .9. Each voter has the option to vote for candidate 1, for candidate 2, or to not vote. (a) Formulate this situation as a Bayesian game. (b) Show that the game has exactly two pure strategy bayesian Nash equilibria, in one of which voter 2 does not vote and in the other of which they always vote for candidate 1. (c) Show that the action of one of the players in the second equilibrium is weakly dominated. (d) Why is "swing voter's curse" an appropriate name for the determinant of voter 2 in the first equilibrium ?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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