Exercise 2.2. A three-man board, composed of A, B, and C, has held hearings on a personnel case involving an officer of the company. This officer was scheduled for promotion but, prior to final action on his promotion, he took a decision that cost the company a good deal of money. The question is whether he should be (1) promoted anyway, (2) denied the promotion, or (3) fired. The board has discussed the matter at length and is unable to reach unanimous agreement. In the course of the discussion it has become clear to all three of them that their separate opinions are as follows: • A considers the officer to have been a victim of bad luck, not bad judgment, and wants to go ahead and promote him but, failing that, would keep him rather than fire him. • B considers the mistake serious enough to bar promotion altogether; he'd prefer to keep the officer, denying promotion, but would rather fire than promote him. C thinks the man ought to be fired but, in terms of personal policy and morale, believes the man ought not to be kept unless he is promoted, i.e., that keeping an officer who has been declared unfit for promotion is even worse than promoting him. To recapitulate, their preferences among the three outcomes are PROMOTE KEEP FIRE A: best middle worst B: worst best middle C: middle worst best Assume that everyone's preferences among the three outcomes are fully evident as a result of discussion. The three must proceed to a vote. Consider the following voting procedure. First A proposes an action (either promote or keep or fire). Then it is B's turn. If B accepts A's proposal, then this becomes the final decision. If B disagrees with A'a proposal, then C makes the final decision (which may be any of the three. promote, keep of fire). Represent this situation as an extensive game with perfect information.
Exercise 2.2. A three-man board, composed of A, B, and C, has held hearings on a personnel case involving an officer of the company. This officer was scheduled for promotion but, prior to final action on his promotion, he took a decision that cost the company a good deal of money. The question is whether he should be (1) promoted anyway, (2) denied the promotion, or (3) fired. The board has discussed the matter at length and is unable to reach unanimous agreement. In the course of the discussion it has become clear to all three of them that their separate opinions are as follows: • A considers the officer to have been a victim of bad luck, not bad judgment, and wants to go ahead and promote him but, failing that, would keep him rather than fire him. • B considers the mistake serious enough to bar promotion altogether; he'd prefer to keep the officer, denying promotion, but would rather fire than promote him. C thinks the man ought to be fired but, in terms of personal policy and morale, believes the man ought not to be kept unless he is promoted, i.e., that keeping an officer who has been declared unfit for promotion is even worse than promoting him. To recapitulate, their preferences among the three outcomes are PROMOTE KEEP FIRE A: best middle worst B: worst best middle C: middle worst best Assume that everyone's preferences among the three outcomes are fully evident as a result of discussion. The three must proceed to a vote. Consider the following voting procedure. First A proposes an action (either promote or keep or fire). Then it is B's turn. If B accepts A's proposal, then this becomes the final decision. If B disagrees with A'a proposal, then C makes the final decision (which may be any of the three. promote, keep of fire). Represent this situation as an extensive game with perfect information.
Chapter1: Making Economics Decisions
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Transcribed Image Text:Exercise 2.2. A three-man board, composed of A, B, and C, has held hearings
on a personnel case involving an officer of the company. This officer was
scheduled for promotion but, prior to final action on his promotion, he took
a decision that cost the company a good deal of money. The question is
whether he should be (1) promoted anyway, (2) denied the promotion, or (3)
fired. The board has discussed the matter at length and is unable to reach
unanimous agreement. In the course of the discussion it has become clear to
all three of them that their separate opinions are as follows:
• A considers the officer to have been a victim of bad luck, not bad
judgment, and wants to go ahead and promote him but, failing that, would
keep him rather than fire him.
• B considers the mistake serious enough to bar promotion altogether; he'd
prefer to keep the officer, denying promotion, but would rather fire than
promote him.
C thinks the man ought to be fired but, in terms of personal policy and
morale, believes the man ought not to be kept unless he is promoted, i.e.,
that keeping an officer who has been declared unfit for promotion is even
worse than promoting him.
To recapitulate, their preferences among the three outcomes are
PROMOTE
KEEP
FIRE
A:
best
middle
worst
B:
worst
best
middle
C:
middle
worst
best
Assume that everyone's preferences among the three outcomes are fully evident
as a result of discussion. The three must proceed to a vote.
Consider the following voting procedure. First A proposes an action (either
promote or keep or fire). Then it is B's turn. If B accepts A's proposal, then this
becomes the final decision. If B disagrees with A'a proposal, then C makes the
final decision (which may be any of the three. promote, keep of fire). Represent
this situation as an extensive game with perfect information.
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