Math 482 (Lecture 12): Game theory and linear
programming
This lecture discusses matrix games and Von Neumann's MiniMax theorem (I do not
believe this is covered in the textbook.)
Wikipedia entry on game theory.
Online video introducing game theory.
Game theory is an umbrella term for analysis of a number of kinds of mathematical
games,
as listed here.
These games model "strategic situations", i.e., ones that demand
decision making.
NONexample of strategic situation:
a (mythical?)
perfect competition
, or a monopoly.
Example of strategic situation:
Airline ticket prices: suppose two airlines (American and
United) have flights from Chicago to San Francisco. How should American price their
flight this week if they don't know what United is going to do?
An admittedly simplistic model of what happens is the following: there's a group of 100
shoppers who only care about price and will go with the cheapest ticket. Say high price is
$3, medium is $2 and low is $1 for both airlines.
In this scenario, the distribution of customers is:
United price
low
United price
medium/expected
United price
high
American price low
50,50
100,0
100,0
American price
medium/expected
0,100
50,50
100,0
American price high
0,100
0,100
50,50
Coverting this to revenue under the assumption a high, medium and low price is $5,$2
and $1 respectively gives:
United price
low
United price
medium/expected
United price
high
American price low
50,50
100,0
100,0
American price
medium/expected
0,100
100,100
200,0
American price high
0,100
0,200
250,250
In class discussion:
What do you do if you're American airlines for next week? What do
you do if you are deciding how to price things for the next year? (How would you
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 Spring '08
 Staff
 Math, Game Theory, John von Neumann, Row, Minimax Theorem, American price

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