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Strategy18Handout

# Strategy18Handout - Bayes Rule Bayes Rule A B A B Universe...

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11/11/2008 1 Bayes Rule AB ± P[A&B] = P[B|A]·P[A] = P[A|B]·P[B] ± P[B|A] = P[A|B]·P[B] / P[A] -Bayes’ Rule Bayes Rule ± Bayes’ Rule P[B|A] = P[A|B]·P[B] / P[A] ± = P[A|B]·P[B] / (P[A|B]·P[B] + P[A|¬B]·P[¬B] ) Universe of Possibility Bayes Rule ± Consider testing for a particular genetic trait ± A: You test positive ± B: You actually have the trait ± Experimental data often gives us information on ± Bayes’ Rule P[B|A] = P[A|B]·P[B] / P[A] ± = P[A|B]·P[B] / (P[A|B]·P[B] + P[A|¬B]·P[¬B] ) ± P[A], P[B], and P[A|B] OR ± P[B], P[A|B], P[A|¬B] Games of Toughness ± We will use Bayesian analysis in finding equilibria to a signaling game ± Drinking beer is costly ± It can serve as a costly signal of toughness Beer-Quiche Game 1 Tough .25 Pete Nick Beer Quiche Nick (-10, -10 ) NF F NF F (0, 0 ) (-16, -10 ) (-6, 0 ) Nature Wimpy .75 Pete Nick Beer Quiche Nick (-5, 5 ) NF F NF F (0, 0 ) (-11, 5 ) (-6, 0 ) Games of Toughness ± We will use Bayesian analysis in finding equilibria to a signaling game ± Nick draws inferences about Pete’s type from Pete’s actions applying Bayes’ Rule ± “Bayesian Updating” ± We can’t mechanically apply rollback… ± Nick’s optimal actions depend on his beliefs about Pete’s type ± Nick’s beliefs depend on Pete’s actions ± Pete’s actions depend on Nick’s beliefs

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11/11/2008 2 Games of Toughness ±
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Strategy18Handout - Bayes Rule Bayes Rule A B A B Universe...

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