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G
AME
T
HEORY IN THE
S
OCIAL
S
CIENCES
Bargaining between a Plaintiff and Defendant with Incomplete Information
In class on Tuesday (11/13), we worked through a bargaining problem between a plaintiff,
P
,
and
a defendant,
D
.
After much work, we said that
the optimal settlement offer was
s =
35. As some students
realized, the probability that this offer would be accepted would be [40(50s)]/20 = 25/20 = 1.25!
But
probabilities have to be between zero and 1, so this cannot be correct. What went wrong? Where did the
professor screw up?
The short answer is that the optimal offer is a “corner solution” and we did not check for this in
class. Checking for corner solutions can be long and tedious. In the artificial setting of class, e.g., in
problems sets, midterms, finals, and at least in principle in examples done in lecture, we will not take the
time to check of corner solutions because the problems
should
be designed so that the optimal offers are
not corner solutions. In the real world outside class, you should always check for corner solutions.
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 Fall '10
 Power

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