Problem Set 10
Econ 159a/MGT522a Ben Polak
Four Problems Due December 5, 2007
Alex and Barry have a joint project.
make these individual investment choices simultaneously. Once made, these investments are
sunk. If noone invests, the project generates a total revenue of $0. If just one of them invests,
then the project generates a (gross) total revenue of $15. If both of them invests, the project
generates a (gross) total revenue of $30.
Alex and Barry then use the following scheme to divide the total project revenue. Each
player simultaneously writes down a ‘share demand’ on a piece of paper. The demands can be
either
1
5
,
1
2
, or
4
5
. If the two ‘share demands’ add up exactly to one then each player is given his
demand. Otherwise, all the money is thrown away.
$10
then the project generates a gross total of
$30
. If Alex then writes down
4
5
and Barry writes down
1
5
then (since this adds up to one) Alex gets his
demand of
$24
(
=
4
5
$30
$14
(i.e.,
$24
minus his initial investment of
$10
), while
Barry gets his demand of $
6
(
=
1
5
$30
±
$4
(i.e.,
$6
minus his initial investment
of
$10
). If Barry had demanded
1
2
while Alex was still demanding
4
5
, then the project money would
have been thrown away and each would simply have lost his initial investment of
$10
.]
Suppose for now that both Alex and Barry are told how much the project has generated
before they make their ‘share demands’.
(a)
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 Fall '08
 BENJAMINPOLAK
 Game Theory, Alex, New Haven, equilibrium strategies

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