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?

.5em;="" "open="">Additional Requirements

Min Pages: 1

Max Pages: 2

Level of Detail: Show all work

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)