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Unformatted text preview: ECON 410 Game Theory Fundamentals – BR Graphs “A wise man is superior to any insults which can be put upon him, and the best reply to unseemly behavior is patience and moderation. “ – Moliere 2 Class 25  Game Theory BR Graphs 3 Class 25  Game Theory BR Graphs 4 Class 25  Game Theory BR Graphs Mixed Strategy Nash Equilibria A strategy profile in which all players are randomizing between strategies and no individual has an incentive to deviate. 5 1, 11, 11, 1 1, 1 Player 2 Tails Head s Tails Heads Player 1 Mixed Strategy NE: A strategy profile in which all players are randomizing between strategies and no individual has an incentive to deviate. Class 25  Game Theory BR Graphs 0.25 0.75 6 1, 11, 11, 1 1, 1 Player 2 Tails Head s Tails Heads Player 1 Mixed Strategy NE: A strategy profile in which all players are randomizing between strategies and no individual has an incentive to deviate. Class 25  Game Theory BR Graphs 0.25 0.75 7 1, 11, 11, 1 1, 1 Player 2 Tails Head s Tails Heads Player 1 Mixed Strategy NE: A strategy profile in which all players are randomizing between strategies and no individual has an incentive to deviate. Class 25  Game Theory BR Graphs 0.25 0.75 8 Class 13  Uncertainty Fundamentals Things: Lottery: 0.25 0.75 vNM Utility: 11 Expected Utility of the Lottery = (1)(.25) + (1)(.75) = 0.50 9 Class 13  Uncertainty Fundamentals Things: Lottery: 0.25 0.75 vNM Utility:1 1 Expected Utility of the Lottery = (1)(.25) + (1)(.75) = 0.50 10 Class 13  Uncertainty Fundamentals 11 1, 11, 11, 1 1, 1 Player 2 Tails Head s Tails Heads Player 1 Mixed Strategy NE: A strategy profile in which all players are randomizing between strategies and no individual has an incentive to deviate. Class 25  Game Theory BR Graphs 0.25 0.75 12 Class 25  Game Theory BR Graphs GroupClicker Question (P): Assume Player 2 is randomizing as shown, below. Specifically, with probability .80 Player 2 is playing Heads and with probability .20 Player 2 is playing Tails. Assuming Player 1 is an expected utility maximizer, should she play Heads or Tails? 1, 11, 11, 1 1, 1 Player 2 Tails Head s Tails Heads Player 1 0.80 0.20 GroupClicker Question (P): Let’s make this question a little harder. Assume Player 2 is randomizing as shown, below. Specifically, with probability Player 2 is playing Heads and with probability (1 ) Player 2 is playing Tails. Assuming Player 1 is an expected utility maximizer, what value of will make Player 1 indifferent between playing Heads and playing Tails? Hint: Solve for the expected utility of playing Heads. Then solve for the expected utility of playing Tails. Lastly, set the expected utilities equal and solve for ....
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 Fall '07
 Codrin
 Game Theory, player, Theory BR Graphs, Game Theory BR

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