lec11 - 1 15.053 Tuesday, March 20 2-person 0-sum (or...

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Unformatted text preview: 1 15.053 Tuesday, March 20 2-person 0-sum (or constant sum) game theory Quotes of the Day My work is a game, a very serious game. -- M. C. Escher (1898 - 1972) Conceal a flaw, and the world will imagine the worst. -- Marcus Valerius Martialis (40 AD - 103 AD) Reveal your strategy in a game, and your outcome will be the worst. -- Professor Orlin (for the lecture on game theory) 2 Game theory is a very broad topic 6.254 Game Theory with Engineering Applications 14.12 Economic Applications of Game Theory 14.122 Microeconomic Theory II 14.126 Game Theory 14.13 Economics and Psychology 14.147 Topics in Game Theory 15.025 Game Theory for Strategic Advantage 17.881 Game Theory and Political Theory 17.882 Game Theory and Political Theory 24.222 Decisions, Games and Rational Choice We will cover 2-person 0-sum game theory for several reasons: 1. It is closely connected to linear programming and duality 2. It introduces some important concepts in game theory 3. I think it is fun. 3 From Marilyn Vos Savants column. Say youre in a public library, and a beautiful stranger strikes up a conversation with you. She says: Lets show pennies to each other, either heads or tails. If we both show heads, I pay you $3. If we both show tails, I pay you $1. If they dont match, you pay me $2. At this point, she is shushed. You think: With both heads 1/4 of the time, I get $3. And with both tails 1/4 of the time, I get $1. So 1/2 of the time, I get $4. And with no matches 1/2 of the time, she gets $4. So its a fair game. As the game is quiet, you can play in the library. But should you? Should she? submitted by Edward Spellman to Ask Marilyn on 3/31/02 Marilyn Vos Savant has a weekly column in Parade. She has the highest recorded IQ on record. I read Marilyn Vos Savants column on a regular basis. Some of my favorite columns of hers are ones that deal with elementary probability or mathematics. 4 2-person 0-sum Game Theory z Two people make decisions at the same time. z The payoff depends on the joint decisions. z Whatever one person wins the other person loses. Marilyn vos Savant answered the question incorrectly. http://www.siam.org/siamnews/06-03/gametheory.pdf 5 6 Payoff Matrix for Vos Savants Game You choose heads or tails The beautiful stranger chooses heads or tails This matrix is the payoff matrix for you, and the beautiful stranger gets the negative.-2 1 3 -2 Heads Tails Heads Tails You Beautiful Stranger 7 Payoff Matrix for Rock-Paper-Scissors Person R chooses a row: either 1, 2, or 3 Person C chooses a column: either 1, 2, or 3 This matrix is the payoff matrix for player R. (And player C gets the negative.) C 1-1-1 1-1 1 Rock Paper Scissors Rock Paper Scissors R 8 Another Payoff Matrix Person R chooses a row: either 1, 2, or 3 Person C chooses a column: either 1, 2, or 3 This matrix is the payoff matrix for player R. (And player C gets the negative.) e.g., R chooses row 3; C chooses column 1 R gets 1; C gets 1 (zero sum) 2-1 1-2-2 1 2 1-2...
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This note was uploaded on 01/17/2012 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.

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lec11 - 1 15.053 Tuesday, March 20 2-person 0-sum (or...

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