4. Consider the following strategic environment involving a firm manager (Manager) and two workers (Worker 1 and Worker 2). The sequence of moves is as follows. In Stage 1, the Manager decides the shares of the total revenues allocated to Worker 1 and Worker 2 (each worker receives the same share of revenues). Two possible sharing rules can be chosen by the Manager: Low Sharing Rule (L, a low percentage of revenues shared with each worker) and High Sharing Rule (H, a high percentage of the revenues share with each worker).
4. Consider the following strategic environment involving a firm manager (Manager) and two workers (Worker 1 and Worker 2). The sequence of moves is as follows. In Stage 1, the Manager decides the shares of the total revenues allocated to Worker 1 and Worker 2 (each worker receives the same share of revenues). Two possible sharing rules can be chosen by the Manager: Low Sharing Rule (L, a low percentage of revenues shared with each worker) and High Sharing Rule (H, a high percentage of the revenues share with each worker).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![4. Consider the following strategic environment involving a firm manager (Manager) and two
workers (Worker 1 and Worker 2).
The sequence of moves is as follows.
In Stage 1, the Manager decides the shares of the total revenues allocated to Worker 1 and
Worker 2 (each worker receives the same share of revenues). Two possible sharing rules
can be chosen by the Manager: Low Sharing Rule (L, a low percentage of revenues shared
with each worker) and High Sharing Rule (H, a high percentage of the revenues share with
each worker).
In Stage 2 (the Effort Stage), after observing the sharing rule chosen by the Manager,
Worker 1 and Worker 2 simultaneously decide whether to "Work Hard" or to "Shirk."
The following two matrices represent the Effort Stage when the Low Sharing Rule (L) is
chosen by the Manager and when the High Sharing Rule (H) is chosen by the Manager. The
payoffs in brackets correspond to the Manager.
Low Sharing Rule (L)
High Sharing Rule (H)
Work Hard
Shirk
Work Hard
Shirk
Work
31, 31
2, 40
Work
82, 82
32, 70
Hard
[206]
[120]
Hard
[104]
[60]
Shirk
40, 2
20, 20
Shirk
70, 32
35, 35
(120]
(60]
[60]
(30]
Represent this strategic envitonment in an extensive form.
a.
b.
Characterize the S.P.N.E. of the game using the Generalized Backward Induction
procedure. Make any necessary assumptions to achieve a unique S.P.N.E Explain your
results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63af03e7-3d9f-4a50-be1c-a596225d5a1b%2Fc7e0de22-539b-429d-ab57-fe8c93dedc9a%2Frllmy9p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Consider the following strategic environment involving a firm manager (Manager) and two
workers (Worker 1 and Worker 2).
The sequence of moves is as follows.
In Stage 1, the Manager decides the shares of the total revenues allocated to Worker 1 and
Worker 2 (each worker receives the same share of revenues). Two possible sharing rules
can be chosen by the Manager: Low Sharing Rule (L, a low percentage of revenues shared
with each worker) and High Sharing Rule (H, a high percentage of the revenues share with
each worker).
In Stage 2 (the Effort Stage), after observing the sharing rule chosen by the Manager,
Worker 1 and Worker 2 simultaneously decide whether to "Work Hard" or to "Shirk."
The following two matrices represent the Effort Stage when the Low Sharing Rule (L) is
chosen by the Manager and when the High Sharing Rule (H) is chosen by the Manager. The
payoffs in brackets correspond to the Manager.
Low Sharing Rule (L)
High Sharing Rule (H)
Work Hard
Shirk
Work Hard
Shirk
Work
31, 31
2, 40
Work
82, 82
32, 70
Hard
[206]
[120]
Hard
[104]
[60]
Shirk
40, 2
20, 20
Shirk
70, 32
35, 35
(120]
(60]
[60]
(30]
Represent this strategic envitonment in an extensive form.
a.
b.
Characterize the S.P.N.E. of the game using the Generalized Backward Induction
procedure. Make any necessary assumptions to achieve a unique S.P.N.E Explain your
results.
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