# Lecture 12: Modeling Introduction to Game Theory.

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Lecture 12: Modeling Introduction to Game Theory

Today’s Plan Unreasonable beliefs in WPBE Excercise

Beer or Quiche Game Example of signaling game – generally two types of players: sender and receiver P1 (sender) is assigned strength by nature known only to him. Two types “Weak” or “Strong” (probabilities ½ and ½). P1 chose his breakfast: Beer or Quiche. P2 observes P1 having breakfast and decides whether to pick up a fight with P1. P2 do not know P1’s strength.

Beer or Quiche Game Peace Fight Nature Weak Strong½ ½ 1, 1 3, 0 0, 0 2, 1 0, 1 2, 0 1, 0 3, 1 Quiche P2[1-p] P2[p] P2[1-p] P1 QuicheBeer Fight Peace

No Separating Equilibrium Option 1: Strong P1 goes for Quiche and Weak for Beer Beliefs of P2 are p=1 of Beer is observed, p=0 otherwise. P2 fights if Beer is observed and stays peaceful if Quiche is observed. Weak P1 would go for beer – Not equilibrium. Option 2: Strong P1 goes for Beer and Weak for Quiche Beliefs of P2 are p=0 of Beer is observed, p=1 otherwise. P2 fights if Quiche is observed and stays peaceful otherwise. Weak P1 would go for beer – Not equilibrium.

Pooling Equilibria E1: Both types of P1 drinks Beer and P2 believes that all Quiche eaters are wimps. World is in peace. E2: Both types of P1 eats Quiche and P2 believes that all Beer drinkers are wimps E2: Why should P2 believe that all Beer drinkers are wimps, when Weak P1 is strictly worse off drinking Beer? Counterintuitive? Does opportunity to have a chat before breakfast change the result? Can Strong P1 convince P2 not to fight him when P1 drinks beer?

Model Abstraction made from the real world in purpose to understand our observations and experience Real world to complex to account for all perspectives. Bounded computational capacity Good enough approximation Drop unimportant elements Cows, weather, husband’s mood,… Keep elements with significant influence on the result Cows, weather, husband’s mood, …

Game Theory and Cold War Cuban Missile Crisis 1958- U.S. deploys missiles in U.K., Italy and Turkey. Sept. 1962 – USSR builds bases for nukes on Cuba. Oct. 1962 – U.S. gets tangible proofs on the bases. U.S. settled military ‘quarantine’ on Cuba. Sequence of ‘chatting’ between Kennedy and Khrushchev USSR withdraw missiles from Cuba. Why USSR pulled back? Complete information vs. incomplete information Or how U.S. prohibition on alcohol deterred USSR from placing nukes on Cuba.

Marriage as Commitment Why do people marry? Marital investments. Prisoners’ dilemma. Marriage with costly divorce results in parreto improvement. Source: Becker (1973) “A Theory of Marriage: Part I”

Divorce Laws Did unilateral divorce law increases divorce rate? Source: Wolfers (2006) “Did Unilateral Divorce Laws Raise Divorce Rates? A reconciliation and New Results”

Crime and Punishment By how much more severe punishment deters crime? Prosecutor vs. judge. Source: Tsuchimoto and Dusek (2010) “Responses to More Severe Punishment in the Courtroom: Evidence from Truth-in-Sentencing Laws.”

Zahavi’s Handicap Principle Why do peacocks have large tails? Contradiction to evolution theory? Is Bill Gates peacock with the largest tail? Donating \$21 billions to his charitable foundation. Source: Richard Conniff “Why We Take Risks”