Lecture12

Lecture12 - C&O 355 Mathematical Programming Fall 2010...

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Unformatted text preview: C&O 355 Mathematical Programming Fall 2010 Lecture 12 N. Harvey What movie is this? What is the location for this scene? Who are the people in this scene? Daniel Kleitman First person with finite Erdos-Bacon number? Two-Player Zero-sum Games Alice and Bob play the following game Alice has m possible actions she can make Bob has n possible actions he can make They both simultaneously choose an action If Alice chooses action i and Bob chooses action j then Bob pays Alice M ij dollars Zero-sum means amount Alice wins equals amount Bob loses Bob Rock Scissors Paper Rock 1-1 Scissors-1 1 Paper 1-1 Alice M http://www.toddlittleton.net/ Randomized Strategies As we know from Rock-Scissors-Paper, we seek randomized choices of actions that optimize the expected payoff Suppose Alice chooses a probability distribution x 2 R m over her actions and Bob chooses a distribution y 2 R n over his actions. (So x 0, i x i = 1, y 0, i y i...
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This note was uploaded on 06/16/2011 for the course CO 355 taught by Professor Harvey during the Winter '10 term at Waterloo.

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Lecture12 - C&O 355 Mathematical Programming Fall 2010...

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