Smith has been injured during an operation. With probability .5 the doctor is guilty of malpractice...

Smith has been injured during an operation. With probability .5 the doctor is guilty of
malpractice and with probability .5 he is innocent. The doctor knows whether or not he is
actually guilty. Smith threatens to sue the doctor. Before the case goes to trial, the doctor can
settle out of court. If the doctor settles, he pays Smith 1,000, Smith pays 1/3 of this 1,000 to her
lawyer, and the doctor does not pay any legal fees. If the doctor does not settle then Smith can
either drop the suit or let the case go to trial. If Smith drops the suit Smith and the doctor each
receive a payoff of 0. If the case goes to trial, the doctor's guilt or innocence will be discovered.
If Smith wins the trial, then (i) she will win 1,000 but will have to give 1/3 of this 1,000 to her
lawyer, and (ii) the doctor will lose the 1,000 he pays Smith and an additional 100 in legal fees.
If Smith loses the trial then she must pay the doctor's legal fees of 100.

(a) Show that this game has all of the basic elements of a signaling game.

(b) Show that this game does not have a separating equilibrium.

(c) Show that this game does not have a pooling equilibrium.

(d) Find the mixed strategy perfect Bayes-Nash equilibrium in this game.

Expert Solution

Rahul Sunny answered 1 year ago

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Smith has been injured during an operation. With probability .5 the doctor is guilty of malpractice...

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