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Unformatted text preview: Nash Equilibria in Mixed Strategies L A T E X file: mixednashmathematicanball — Daniel A. Graham <[email protected]>, June 22, 2005 RockPaperScissors Since the game is symmetric, we’ll solve for the probabilities that player 2 (column chooser) must use to make player 1 (row chooser) indifferent. The probabilities that player 1 must use to make player 2 indifferent will be the same. pay1 = {{ , 1 , 1 } , { 1 , , 1 } , { 1 , 1 , }} ; In: pay1//MatrixForm  1 1 1 1 1 1 Out: prob2 = { q1 , q2 , q3 } ; In: The expected payoffs to player 1: ep1 = pay1 . prob2 In: { q2 + q3 , q1 q3 , q1 + q2 } Out: The expected payoffs to each of player 1’s 3 actions (rock, paper, scissors) must be equal, and thus must all equal some common c, and the probabilities used by player 2 must add up to 1. The probabilities must also be nonnegative but we’ll check for that later....
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This document was uploaded on 10/20/2011.
 Spring '09
 Physics

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