(Answered)-The following game is a styled representation of the strategic - (2025 Updated Original AI-Free Solution

Question

1. The following game is a styled representation of the strategic interaction between a principal (who delegates some authority to an agent and can choose whether or not to audit that agent?s effort in any period) and an agent (who chooses whether to ?work? or ?shirk?). An audit is costly to the principal, but he doesn?t have to pay the agent if he detects shirking. The particular payoffs arise from the following values associated with the relevant activities. The principal earns 4 if his agent works, but doesn?t earn anything if the agent shirks. He pays the agent 3 to work, but if he audits and catches the agent shirking he doesn?t have to pay the agent anything. An audit costs one unit to conduct; thus if the agent works and the principal audits, the principal nets out 0. It costs the agent 2 to do his work, so he of course prefers to shirk and not be audited (earning his wage without doing anything!) but fears getting audited and earning 0.

Principal:
Audit ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?Don?t Audit

(1, 0)	(1, 1)
(0, ?1)	(3, ?3)

?Agent: Work

? ? ? ? ? ? ? Shirk

1. a) ?Does either individual have a strategy that is optimal no matter what the other individual plays (as in the Prisoner?s Dilemma)??
2. b) ?Are any of the four cells equilibria??
3. c) ?What percentage of the time must the principal inspect to make the agent indifferent between working and shirking? (
4. d) ?What percentage of the time must the agent work to make the principal indifferent between auditing and not auditing??

1.
The following game is a styled representation of the strategic interaction between a principal (who
delegates some authority to an agent and can choose whether or not to audit that agent?s...