economics 202 intermediate microeconomic theory l.
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Economics 202: Intermediate Microeconomic Theory Questions? Sundance Confess Don’t Confess Confess Butch Don’t Confess 5 10 1 5 2 1 10 2 The Prisoner’s Dilemma Butch Cassidy & the Sundance Kid (classic film, rent it tonight) rob a train.

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slide2

Sundance

Confess

Don’t Confess

Confess

Butch

Don’t

Confess

5

10

1

5

2

1

10

2

The Prisoner’s Dilemma

  • Butch Cassidy & the Sundance Kid (classic film, rent it tonight) rob a train.
  • They get caught, are held in separate rooms & each offered this deal:

1. If both confess to stiffer charge of attempted murder, both get 5 years.

2. If neither confesses, both get 2 years for robbery.

3. If only one confesses, the rat gets lenient 1 year, other gets 10 years.

  • Confess is dominant strategy for each.
  • But this makes them both worse off than if they could collude and both not confess, so why not collude?
    • Because it’s not in their self-interest.
    • Confession is not because they believe the other guy will confess also!
  • When might they collude?
    • Repeated game
  • Point is that self-interested behavior can sometimes lead to less than optimal outcomes for all
  • Can apply to USA vs. USSR, elections, health care, etc.
slide3

Game Theory

  • 4 main categorizations
    • Static vs. Dynamic
    • Complete vs. Incomplete info
  • Static games with complete information
    • Cournot duopoly
    • Iterated elimination of dominated strategies (how should you not play!)
    • Nash equilibrium

Information

Complete

Incomplete

Bayesian Nash

Equilibrium

Nash

Equilibrium

Static

Timing

Backward

Induction

Perfect Bayesian

Equilibrium

Dynamic

B

Left

Middle

Right

Up

A

Game 1

  • Game 1 and Game 2
    • Iterated elimination of D.S. solution?
  • Game 1 and Game 2
    • Unique Nash equilibrium?
    • Unique Nash equilibrium is not always efficient, e.g. Prisoner’s Dilemma

Down

B

L

M

R

T

A

Game 2

M

B

slide4

Game Theory

  • “The Dating Game”
    • Multiple Nash equilibria
    • Nash equilibrium concept loses appeal
  • “Copycat Game”
    • No Nash equilibrium
    • Players want to outguess the other
    • Introduce mixed strategies (in contrast to pure strategies)

Information

Complete

Incomplete

Bayesian Nash

Equilibrium

Nash

Equilibrium

Static

Timing

Backward

Induction

Perfect Bayesian

Equilibrium

Dynamic

Pat

Red

White

Steak

Chris

Dating Game

  • Mixed Strategy = a probability distribution over some or all of a player’s pure strategies
  • Mixed strategies can add Nash equilbria
  • Result: Any game with finite # players who have finite # pure strategies has a Nash equilibrium (possibly utilizing mixed strategies)

Chicken

Jill

Inside

Outside

Inside

Jack

Copycat Game

Outside

slide5

Game Theory

  • Dynamic, complete 2-player sequential move game
  • Order of play
    • Player 1 chooses action a1
    • Player 2 observes a1 and then chooses a2
    • Players receive their payoffs U1(a1,a2) & U2(a1,a2)
  • Examples
    • Stackelberg-version of Cournot duopoly
    • Trust Game -- equilibrium?

Information

Complete

Incomplete

Bayesian Nash

Equilibrium

Nash

Equilibrium

Static

Timing

Backward

Induction

Perfect Bayesian

Equilibrium

Dynamic

Player 2

Honor

Betray

Trust

Player 1

Trust Game

(normal form)

  • Dynamic, simultaneous move (or infinite horizon) games requires an extension of backward induction called subgame-perfect Nash equilibrium

Not trust

Player 1

Trust Game

(extensive form)

Not trust

Trust

Player 2

0,0

Honor

Betray

1,1

-1, 2

slide6

B

Loudly

Softly

Loudly

7, 5

5, 4

A

Softly

6, 4

6, 3

Game Theory

  • “The Dormitory Game”
    • Write extensive form if simultaneous game
    • Write extensive & normal forms if A chooses first