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slide22-Oct21 - ECON 401 Game theory normal-form games and...

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ECON 401: Game theory: normal-form games and extensive-form games Siyang Xiong Rice University October 21, 2011 Xiong (Rice University) ECON 401 October 21, 2011 1 / 20

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Game theory What is a game? multi-agent decision making; an agent°s payo/ depends not only on his own action, but also on others°actions. e.g., chess; e.g., a football game; e.g., a ±rm is playing a game; game theory: a theory about decision making under strategic situations. What is the goal of game theory? make predictions on a strategic situation; for example: prisoner°s dilemma; explain a social phenomenon; for example: the modi±ed prisoner°s dilemma described above. Why game theory is important? Xiong (Rice University) ECON 401 October 21, 2011 2 / 20
example: meet in new york two tourists in new york try to meet with each other; there are two possible locations to meet: empire state building and grand central station they simultanenous choose to go to one of the two locations if they go to the same location, i.e., either the empire state builiding or the grand central stateion, both players get \$10; if they go to di/erent locations, both players get \$0; the payo/ is described as follows: empire state building grand central station empire state building 10 , 10 0 , 0 grand central station 0 , 0 10 , 10 Xiong (Rice University) ECON 401 October 21, 2011 3 / 20

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example: matching pennies two players, each owns a penny they simultanenous show the face of the penny, if the faces of the pennies match i.e., (head, head) or (tail, tail), player 1 gets both pennies, and player 2 gets none. if the faces of the pennies do not match i.e., (head, tail) or (tail, head), player 2 gets both pennies, and player 1 gets none. the payo/ is described as follows: head tail head 2 , ° 2 ° 2 , 2 tail ° 2 , 2 2 , ° 2 Xiong (Rice University) ECON 401 October 21, 2011 4 / 20
example: battle of sex a couple plan to go out tonight.

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