A rm has two divisions, each of which has its own manager. Managers of these
divisions are paid according to their eort in promoting productivity in their divisions,
which is judged by comparison with other managers and other divisions. If both
managers are judged as having expended high eort,” each earns $150,000/year. If
both are judged to have expended low eort,” each earns $100,000/year. But if
one of the two managers shows high eort” while the other shows low eort,” the
high eort” manager is paid $150,000 plus a $50,000 bonus, while the second (low
eort”) manager gets a reduced salary of $80,000. Managers make their eort decisions
independently and without knowledge of the other manager’s choices.
(a) Assume that expending eort is costless to the managers and draw the payo
table for this game. Find the nash equilibrium of the game and explain whether
the game is a prisoners’ dilemma.
(b) Now suppose that expending high eort is costly to the mangers (such as a costly
signal of quality). In particular, suppose that high eort” costs an equivalent of
$60,000/year to a manager that chooses this eort level. Draw the game table for
this new version of the game and nd the Nash equilibrium. Explain whether the
game is a prisoners’ dilemma and how it has changed from the game in part a.
(c) If the cost of high eort is equivalent to $80,000/year, how does the game change
from that described in part b? What is the new equilibrium? Explain whether
the game is a prisoners’ dilemma and how it has changed from the games in part
a and b.
(d) Assume now that the owner of the rm can’t actually observe manager eort, but
instead determines eort based on relative output of the two divisions, meaning
that the manager with the division that produces the most is assumed to have
provided the highest eort. If the payos are the same in part c, does this change
the outcome of the game? If the managers play this game repeatedly, does it
matter whether eort is directly observable?
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Other Requirements: The question belongs to the Behavioral Economics, so please focus on the subject, and answer everything in the question(include drawing table or drawing graph)
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