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