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Lecture12

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

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C&O 355 Mathematical Programming Fall 2010 Lecture 12 N. Harvey

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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 0 1 -1 Scissors -1 0 1 Paper 1 -1 0 Alice M http://www.toddlittleton.net/

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

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