25_GameTheoryBRFunctions

25_GameTheoryBRFunctions - ECON 410 Game Theory...

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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, -1-1, 1-1, 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, -1-1, 1-1, 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, -1-1, 1-1, 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: 1-1 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, -1-1, 1-1, 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 Group-Clicker 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, -1-1, 1-1, 1 1, -1 Player 2 Tails Head s Tails Heads Player 1 0.80 0.20 Group-Clicker Question (P): Lets 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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25_GameTheoryBRFunctions - ECON 410 Game Theory...

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