mitting a crime. Suppose that the trial involves evidence production by both parties and that by producing evidence, a litigant increases the probability of winning the trial. Specifically, suppose that the probability that the defen- dant wins is given by ep/(ep + ep), where e, is the expenditure on evidence production by the defendant and ep is the expenditure on evidence produc- tion by the prosecutor. Assume that ep and ep are greater than or equal to 0. The defendant must pay 8 if he is found guilty, whereas he pays 0 if he is found innocent. The prosecutor receives 8 if she wins and O if she loses the case. (a) Represent this game in normal form. (b) Write the first-order condition and derive the best-response function for each player. (c) Find the Nash equilibrium of this game. What is the probability that the defendant wins in equilibrium. (d) Is this outcome efficient? Why?
mitting a crime. Suppose that the trial involves evidence production by both parties and that by producing evidence, a litigant increases the probability of winning the trial. Specifically, suppose that the probability that the defen- dant wins is given by ep/(ep + ep), where e, is the expenditure on evidence production by the defendant and ep is the expenditure on evidence produc- tion by the prosecutor. Assume that ep and ep are greater than or equal to 0. The defendant must pay 8 if he is found guilty, whereas he pays 0 if he is found innocent. The prosecutor receives 8 if she wins and O if she loses the case. (a) Represent this game in normal form. (b) Write the first-order condition and derive the best-response function for each player. (c) Find the Nash equilibrium of this game. What is the probability that the defendant wins in equilibrium. (d) Is this outcome efficient? Why?
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.15P
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Transcribed Image Text:6. Imagine that a zealous prosecutor (P) has accused a defendant (D) of com-
mitting a crime. Suppose that the trial involves evidence production by both
parties and that by producing evidence, a litigant increases the probability
of winning the trial. Specifically, suppose that the probability that the defen-
dant wins is given by ep/(ep + ep), where ep is the expenditure on evidence
production by the defendant and ep is the expenditure on evidence produc-
tion by the prosecutor. Assume that ep and ep are greater than or equal to
0. The defendant must pay 8 if he is found guilty, whereas he pays 0 if he
is found innocent. The prosecutor receives 8 if she wins and 0 if she loses
the case.
(a) Represent this game in normal form.
(b) Write the first-order condition and derive the best-response function for
each player.
(c) Find the Nash equilibrium of this game. What is the probability that the
defendant wins in equilibrium.
(d) Is this outcome efficient? Why?
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