Summary of previous lectures

1
Summary of previous lectures

• How to treat markets which exhibit normal
  behaviour (lecture 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?

2
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.

3
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?

4
Perfectly rational solution
5
El-Farol bar problem

• Imperfect information you only know if you got a
  table or not.
• You gather information from the experience of
  others.

6
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 dont come back
• Interaction function

Schelling (1978) Micromotives and Macrobehaviour
7
Simulations of bar populations
b6
Beach visitors (at )
time
n4000 sites at the beach
Bk1000 b6
8
Simulations of bar populations
b6
Beach visitors (at )
time
n4000 sites at the beach
Bk1000 b8
9
Simulations of bar populations
b6
Beach visitors (at )
time
n4000 sites at the beach
Bk1000 b20
10
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

11
b6
at1
at
12
Simulations of bar populations
b6
Beach visitors (at )
time
n4000 sites at the beach
Bk1000 b6
13
Simulations of bar populations
b6
Beach visitors (at )
time
n4000 sites at the beach
Bk1000 b8
14
Simulations of bar populations
b6
Beach visitors (at )
time
n4000 sites at the beach
Bk1000 b20
15
Period doubling route to chaos
16
Are stock markets chaotic?
17
Are stock markets chaotic?
Not really like the distributions we saw in
lectue 1.
18
El-Farol bar problem
Arthur 1994
19
El-Farol bar problem
Arthur 1994
20
El-Farol bar problem
Arthur 1994
21
Minority game
Brain size is number of bits in signal (3)
Challet and Zhang 1997
22
Minority game
Challet and Zhang 1997
23
Minority game
Challet and Zhang 1998
24
Break
25
Do humans copy each other?
26
Aschs experiment
Asch (1955) Scientific American
27
Aschs experiment
Asch (1955) Scientific American
28
Aschs experiment
Asch (1955) Scientific American
29
Milgrams experiment
30
Milgrams experiment
Hale (2008)
31
Milgrams experiment
Milgram Toch (1969)
32
Irrationality in financial experts

• Keynes beauty contest
• Behaviuoral economics (framing, mental
  accounting, overconfidence etc.). Thaler,
  Kahneman, Tversky etc.
• Herding? (less experimental evidence)

33
Consequences of copying
34
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.