# lecture 12 - Math 482(Lecture 12 Game theory and linear...

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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. NON-example 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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lecture 12 - Math 482(Lecture 12 Game theory and linear...

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