summary of previous lectures 1.how to treat markets which exhibit normal behaviour (lecture 2)....

Summary of previous lectures

1. How to treat markets which exhibit ’normal’ behaviour (lecture 2).

2. Looked at evidence that stock markets were not always ’normal’, stationary nor in equilibrium (lecture 1).

Is it possible to model non-normal markets?

From individual behaviour to market dynamics

Describe how individuals interact with each other.

Predict the global dynamics of the markets.

Test whether these assumptions and predictions are consistent with reality.

El-Farol bar problem

• Consider a bar which has a music night every Thursday. We define a payoff function, f(x)=k-x, which measures the ‘satisfaction’ of individuals at the bar attended by a total of x patrons.

• The population consists of n individuals. What do we expect the stable patronage of the bar to be?

Perfectly rational solution

El-Farol bar problem

• Imperfect information: you only know if you got a table or not.

• You gather information from the experience of others.

El-Farol bar problem

• If you find your own ’table’ then tell b others about the bar. If you have to fight over a ’table’ then don’t come back

• Interaction function

Schelling (1978) Micromotives and Macrobehaviour

Simulations of bar populationsb=6

time

Beach visitors

(at )

n=4000 sites at the beach0 5 10 15 20 25 30 35 40 45 50

0

1000

2000

3000

4000

5000

6000

7000

Time: t

Pop

ulat

ion

:xt

Bk=1000 b=6

Simulations of bar populationsb=6

time

Beach visitors

(at )

n=4000 sites at the beach

Bk=1000 b=8

0 5 10 15 20 25 30 35 40 45 500

1000

2000

3000

4000

5000

6000

7000

Time: t

Pop

ulat

ion

:xt

Simulations of bar populationsb=6

time

Beach visitors

(at )

n=4000 sites at the beach

Bk=1000 b=20

0 5 10 15 20 25 30 35 40 45 500

1000

2000

3000

4000

5000

6000

7000

Time: t

Pop

ulat

ion

:xt

A derivation

Interaction function

The mean population on the next generation is given by

where pk is the probability that k individuals choose a particular site.

If pk is totally random (i.e. indiviudals are Poisson distributed) then

0

5000

10000

15000

20000

25000

0 4000 8000 12000 16000

b=6

at+1

at

Simulations of bar populationsb=6

time

Beach visitors

(at )

n=4000 sites at the beach

0 5 10 15 20 25 30 35 40 45 500

1000

2000

3000

4000

5000

6000

7000

Time: t

Pop

ulat

ion

:xt

Bk=1000 b=6

0 1000 2000 3000 4000 5000 6000 70000

1000

2000

3000

4000

5000

6000

7000

Population at time t: xt

Pop

ulat

ion

at t

ime

t+1:

x t+1

Simulations of bar populationsb=6

time

Beach visitors

(at )

n=4000 sites at the beach

Bk=1000 b=8

0 5 10 15 20 25 30 35 40 45 500

1000

2000

3000

4000

5000

6000

7000

Time: t

Pop

ulat

ion

:xt

0 1000 2000 3000 4000 5000 6000 70000

1000

2000

3000

4000

5000

6000

7000

Population at time t: xt

Pop

ulat

ion

at t

ime

t+1:

x t+1

Simulations of bar populationsb=6

time

Beach visitors

(at )

n=4000 sites at the beach

Bk=1000 b=20

0 5 10 15 20 25 30 35 40 45 500

1000

2000

3000

4000

5000

6000

7000

Time: t

Pop

ulat

ion

:xt

0 1000 2000 3000 4000 5000 6000 70000

1000

2000

3000

4000

5000

6000

7000

Population at time t: xt

Pop

ulat

ion

at t

ime

t+1:

x t+1

Period doubling route to chaos

Are stock markets chaotic?

Are stock markets chaotic?

Not really like the distributions we saw in lectue 1.

El-Farol bar problem

Arthur 1994

El-Farol bar problem

Arthur 1994

El-Farol bar problem

Arthur 1994

Minority game

Challet and Zhang 1997

Brain size is number of bits in signal (3)

Minority game

Challet and Zhang 1997

Minority game

Challet and Zhang 1998

Break

Do humans copy each other?

Asch’s experiment

Asch (1955) Scientific American

Asch’s experiment

Asch (1955) Scientific American

Asch’s experiment

Asch (1955) Scientific American

Milgram’s experiment

Milgram’s experimenta

b

c

a

b

c

Hale (2008)

Milgram’s experiment

Milgram & Toch (1969)

Irrationality in financial experts

• Keynes beauty contest

• Behaviuoral economics (framing, mental accounting, overconfidence etc.). Thaler, Kahneman, Tversky etc.

• Herding? (less experimental evidence)

Consequences of copying

Summary

• Markets can be captured by some simple models.

• These models in themselves exhibit complex and chaotic behaviours.

• In pariticular, models of positive feedback could be used to explain certain crashes.