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slide21-oct19 - ECON 401 Game theory introduction Siyang...

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Unformatted text preview: ECON 401: Game theory: introduction Siyang Xiong Rice University October 18, 2011 Xiong (Rice University) ECON 401 October 18, 2011 1 / 16 one example a &rm uses one iput x . & / to produce two outputs y . & / , z . & / by the following technology: y 2 C z 2 ¡ x . The price for x , y , z are 1, 2, 3 respectively. Suppose the &rm tries to maximize pro&t. What is the optimal production plan? Xiong (Rice University) ECON 401 October 18, 2011 2 / 16 one example the &rm solves max x , y , z [ 2 y C 3 z & x ] s.t. x ¡ I y ¡ I z ¡ I x & y 2 & z 2 ¡ I Xiong (Rice University) ECON 401 October 18, 2011 3 / 16 multi-person decision making & game theory the example above only concerns one-person decision. Usually, in real-life economics, more than two person are involved in decision making. the modi¡ed example: two ¡rms uses one iput x . & / to produce two outputs y . & / , z . & / by the following technology: y 2 C z 2 ¡ x . let . x 1 , y 1 , z 1 / and . x 2 , y 2 , z 2 / denote the input-output for ¡rm 1 and 2 respectively. the prices p x . x 1 C x 2 / , p y . y 1 C y 2 / , p z . z 1 C z 2 / for x , y , z depends on the total quantity of each good. both ¡rms try to maximize their pro¡t. what are their production plans? Xiong (Rice University) ECON 401 October 18, 2011 4 / 16 multi-person decision making & game theory given . x 2 , y 2 , z 2 / , ¡rm 1 solves max . x 1 , y 1 , z 1 / [[ p y . y 1 C y 2 / ] & y 1 C [ p z . z 1 C z 2 / ] & z 1 ¡ [ p x . x 1 C x 2 / ] & x 1 ] s.t....
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This note was uploaded on 02/09/2012 for the course ECON 401 taught by Professor Siyang during the Spring '11 term at Rice.

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slide21-oct19 - ECON 401 Game theory introduction Siyang...

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