Bayesian Game Two generals approach the city from two different directions. Each general observes the strength of the city fortifications from his own side. The fortifications are either weak or strong. General i believes that the fortifications on the other side of the city are strong with probability πi. Each general must make a decision whether to attack the city or not. The generals know that the attack is successful if and only if both generals attack simultaneously and the fortifications are weak. Suppose that the payoff from successful attack is 1. If a general attacks and the attack is not successful, his payoff is equal to -1. If the general does not attack, his payoff is 0. a. Consider the strategy of general iin which he attacks if and only if the fortifications are weak. Compute also the payoff when he believes the fortifications are strong. b. For what values of the parameters does there exist a Bayesian Nash equilibrium in which the two generals never attack? c. For what values of the parameters does there exist a Bayesian Nash equilibrium in which the two generals attack with positive probability? What is the probability that the attack is successful?
Bayesian Game Two generals approach the city from two different directions. Each general observes the strength of the city fortifications from his own side. The fortifications are either weak or strong. General i believes that the fortifications on the other side of the city are strong with probability πi. Each general must make a decision whether to attack the city or not. The generals know that the attack is successful if and only if both generals attack simultaneously and the fortifications are weak. Suppose that the payoff from successful attack is 1. If a general attacks and the attack is not successful, his payoff is equal to -1. If the general does not attack, his payoff is 0. a. Consider the strategy of general iin which he attacks if and only if the fortifications are weak. Compute also the payoff when he believes the fortifications are strong. b. For what values of the parameters does there exist a Bayesian Nash equilibrium in which the two generals never attack? c. For what values of the parameters does there exist a Bayesian Nash equilibrium in which the two generals attack with positive probability? What is the probability that the attack is successful?
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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Not use ai please
Transcribed Image Text:Bayesian Game
Two generals approach the city from two different directions. Each general observes the strength of the city fortifications
from his own side. The fortifications are either weak or strong. General i believes that the fortifications on the other side
of the city are strong with probability πi. Each general must make a decision whether to attack the city or not. The
generals know that the attack is successful if and only if both generals attack simultaneously and the fortifications are
weak. Suppose that the payoff from successful attack is 1. If a general attacks and the attack is not successful, his payoff
is equal to -1. If the general does not attack, his payoff is 0.
a. Consider the strategy of general iin which he attacks if and only if the fortifications are weak. Compute also the payoff
when he believes the fortifications are strong.
b. For what values of the parameters does there exist a Bayesian Nash equilibrium in which the two generals never
attack?
c. For what values of the parameters does there exist a Bayesian Nash equilibrium in which the two generals attack with
positive probability? What is the probability that the attack is successful?
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