[Adverse Selection] Each of the two players receives an envelope, in which there is an amount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in two envelopes are independent. After receiving the envelope, each individual can check exactly how much money is put in his/her own envelope. Then each player has the option to exchange his/her envelope for the other individual's prize. The decisions are made simultaneously. If both individuals agree to exchange, then the envelopes are exchanged; otherwise, if at least one player chooses not to exchange, each individual keeps his/her own envelope and receives its attached sum of money. a. Model this game as a static Bayesian game (write the normal form representation) and find the Bayesian Nash equilibrium. b. Consider a new game where the probability distribution of money in each envelope is changed. The amount is equal to $100 with probability 90%, and is equal to each number in $0, $1, $2, ... ,$99 with probability 0.1%. What is the optimal strategy in the Bayesian Nash equilibrium?
[Adverse Selection] Each of the two players receives an envelope, in which there is an amount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in two envelopes are independent. After receiving the envelope, each individual can check exactly how much money is put in his/her own envelope. Then each player has the option to exchange his/her envelope for the other individual's prize. The decisions are made simultaneously. If both individuals agree to exchange, then the envelopes are exchanged; otherwise, if at least one player chooses not to exchange, each individual keeps his/her own envelope and receives its attached sum of money. a. Model this game as a static Bayesian game (write the normal form representation) and find the Bayesian Nash equilibrium. b. Consider a new game where the probability distribution of money in each envelope is changed. The amount is equal to $100 with probability 90%, and is equal to each number in $0, $1, $2, ... ,$99 with probability 0.1%. What is the optimal strategy in the Bayesian Nash equilibrium?
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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[Adverse Selection] Each of the two players receives an envelope, in which there is an
amount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in two
envelopes are independent. After receiving the envelope, each individual can check exactly
how much money is put in his/her own envelope. Then each player has the option to exchange
his/her envelope for the other individual's prize. The decisions are made simultaneously. If
both individuals agree to exchange, then the envelopes are exchanged; otherwise, if at least
one player chooses not to exchange, each individual keeps his/her own envelope and receives
its attached sum of money.
a. Model this game as a static Bayesian game (write the normal form
representation) and find the Bayesian Nash equilibrium.
b. Consider a new game where the probability distribution of money in each
envelope is changed. The amount is equal to $100 with probability 90%, and is equal
to each number in $0, $1, $2, ... ,$99 with probability 0.1%. What is the optimal strategy in the Bayesian Nash equilibrium?
amount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in two
envelopes are independent. After receiving the envelope, each individual can check exactly
how much money is put in his/her own envelope. Then each player has the option to exchange
his/her envelope for the other individual's prize. The decisions are made simultaneously. If
both individuals agree to exchange, then the envelopes are exchanged; otherwise, if at least
one player chooses not to exchange, each individual keeps his/her own envelope and receives
its attached sum of money.
a. Model this game as a static Bayesian game (write the normal form
representation) and find the Bayesian Nash equilibrium.
b. Consider a new game where the probability distribution of money in each
envelope is changed. The amount is equal to $100 with probability 90%, and is equal
to each number in $0, $1, $2, ... ,$99 with probability 0.1%. What is the optimal strategy in the Bayesian Nash equilibrium?
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