Lecture 12:Modeling
Introduction to Game Theory
Today’s PlanUnreasonable beliefs in WPBEExcercise
Beer or Quiche GameExample of signaling game – generally two
types of players: sender and receiverP1 (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[p]
P2[1-p]P1
P1
QuicheBeer
Beer
Fight Fight
Fight
PeacePeace
Peace
No Separating EquilibriumOption 1:
Strong P1 goes for Quiche and Weak for BeerBeliefs 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 QuicheBeliefs 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 EquilibriaE1: 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?
ModelModel
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 approximationDrop unimportant elements
Cows, weather, husband’s mood,…Keep elements with significant influence on the
resultCows, weather, husband’s mood, …
Game Theory and Cold WarCuban 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
KhrushchevUSSR 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 CommitmentWhy 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 LawsDid unilateral divorce law increases divorce
rate?Source: Wolfers (2006) “Did Unilateral Divorce Laws
Raise Divorce Rates? A reconciliation and New Results”
Crime and PunishmentBy 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 PrincipleWhy 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”
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