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Unformatted text preview: Section 1: Some Basics of Game Theory Daniel Egel September 7, 2008 1 Strictly Dominant Strategies Consider the following 3 × 3 game where Player 1 has to choose either { U,M,D } and Player 2 has to choose either { L,M,R } . II L M R I U 3 , 9 , 6 2 , 8 M 2 , 1 3 , 4 3 , 6 D 4 , 3 5 , 1 6 , 2 Let’s do a quick iterative elimination of strictly dominated strategies... Player I : 1. What are the possible payoffs if player I plays U ? 2. Does U strictly dominate D ? M ? 3. Does M strictly dominate U ? D ? 4. Does D strictly dominate U ? M ? 5. What can we say about Player I ’s behavior? Player II : 1. Are any of Player II ’s strategies strictly dominated conditional on our knowledge of player I ’s behavior? 2. What can we say about Player II ’s behavior? Finish the game! What is the result that we find about the actions of these two players? If you finished early, redo our above analysis but start with Player II . Do you get the same result? 1 2 Weakly Dominated Strategies Lets consider a different version of the above game... II L M R I U 3 , 5 , 6 2 , 8 M 2 , 1 5 , 4 3 , 6 D 4 , 3 5 , 2 6 , 2 1. Does either player have any strictly dominated strategies? 2. Does either player have any weakly dominated strategies? Which ones are they and why are they called weakly dominated? 3. Solve this game by iterative deletion of weakly dominated strategies? 3 A Game from the “Real” World So here is a game that I actually have thought about from time to time. And was thinking about when I write these notes as is as follows......
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 Fall '10
 Power
 Game Theory, strictly dominated strategies, weakly dominated strategies, Daniel Egel

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