University of Illinois MBA Program
John P. Conley
Spring 2002
1
MBA 405B
Problem set 1
Due: Monday, April 08, 2002, 5:00pm
1. There are three passengers on a ship sailing across the Atlantic who are carrying large
sums of money.
Suppose passenger A has $1000, passenger B has $1500 and passenger
C has $2000. They each put their money in separate envelopes and give them to captain
who puts them in a chest for safekeeping.
One night the ship is caught in a storm and the
chest is broken open.
The captain picks up all the money the next day, but does not know
much each of the three passengers gave him originally. He proposes the following solution.
He asked each passenger to write down how much money they originally put into their
envelope.
They are to do this at the same time, without speaking to one another.
If the
numbers the agents write down add up to the total amount of money the captain picked up
(assume he managed to find all $4500) then the captain gives each passenger what he
claims he put in.
Otherwise, the captain throws the money into ocean and the passengers
get nothing.
a. Write this out as a formal oneshot game.
Note that there are three players (the
passengers) and that the captain is just a mediator who defines the strategy spaces
and payoff functions of the agents.
I={A,B,C};
S
i
={$0 to infinity} (same for all passengers)
F
i
= $s
i
if s
A
+ s
B
+ s
C
= 4500
(same for all passengers)
$0
otherwise
b.
Is truth telling a Nash equilibrium?
Why or why not?
Yes.
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 Spring '08
 Landsburg
 Game Theory, Subgame perfect equilibrium, John P. Conley, Illinois MBA Program, University of Illinois MBA

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