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”