Game Theory Exercises
Solving Structured Games
• The underlying principle is to
– look forward to determine the outcomes that will result
from your own and competitors’ actions
– Reason backward to find the best decision
• In all of these games it is best to play the game
as it is written (not assuming some other
conditions than those which are given) After you
have played the game, then you can start to
think about how the game could be changed to
get a more favorable result.
Group paper instructions
• This group exercise is due on October 27
– You should choose your own group (about 4-5
member teams seem to work best)
– Solve each of the following game situations
• Tell how the game will turn out (Nash equilibrium)
• Explain how you got your answer
– Each of the game solutions should only
require about one page
– Have fun!
Hot Dog Stands on a
Beach
Oscar and Meyer decide to sell hot dogs on a beach. They
are required to sell the hot dogs at the same price and
the hot dogs are undifferentiated. The sunbathers are
distributed equally along the beach. Where should
Oscar and Meyer locate their hot dog stands?
The Prisoner’s Dilemma
Two vagrants, Al and Joe, have been arrested for vagrancy. The
DA suspects them of complicity in a robbery, but she doesn’t have
enough evidence to convict them. (Al and Joe don’t know this for
sure.) The DA interrogates each of them separately and offers
the following deal: “If you implicate your friend, I’ll reduce your
charge to being an accomplice. If you don’t, I will throw the book
at you.” Assume the relevant prison times (in months) are as
follows:
Al
Joe
Talk
Don’t talk
Talk
(-8, -8)
(0, -15)
Don’t talk
(-15, 0)
(-1, -1)
The Rational Pigs
A big pig and a little pig are in a long, narrow pen. There is a lever at one end of
the pen which, when pressed, dispenses 6 units of food into a trough at the other
end of the pen. Thus, if either pig presses the lever it must run to the other end
of the pen before it can eat. By the time it gets there, the other pig may have
eaten some or most of the food. The big pig is able to prevent the little pig from
getting any of the food when both are at the trough. Assume it requires energy
equivalent to ½ unit of food for either pig to run from one end of the pen to the
other. If both of the pigs press the lever, the subordinate pig is faster than the
dominant pig and can eat two units of food before the dominant pig gets to the
food. The rest of payoffs are listed below. How will this game turn out?
Big Pig:
Little Pig:
Press
Don’t Press
Press
(1.5, 3.5)
(-0.5, 6)
Don’t Press
(5, 0.5)
(0, 0)
Boeing, Airbus and the Superjumbo Aircraft
• Boeing and Airbus are considering building a superjumbo aircraft (@600 seats)
• It is a very expensive and risky proposition. All the
numbers in the following payoff matrix are $billions
• Boeing must pay all of its own development costs
• Airbus will receive a development subsidy of $5 billion
from the European Union
• The introduction of a super-jumbo aircraft (by either firm)
will impact the companies current product lines
– Boeing will lose about half of its 747 sales (- $6 billion)
– Airbus will lose less (-$2 billion)
• The forecasted market for the super-jumbo is $15 billion
• The payoff matrix is computed on the next slide.
Boeing, Airbus and the
super-jumbo airframe (1991)
Boeing
(A/B)
Airbus
Develop
Develop
(6-8+5=3 /
9-8=1)
Doesn’t
Develop
(-2/15-8=7)
Doesn’t Develop
(15-3=12/ -6)
(-1/12)
Market =$15b, Development Cost=$8b, Airbus subsidy=$5b