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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?

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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.

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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?

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Perfectly rational solution

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El-Farol bar problem Imperfect information: you only know if you got a table or not. You gather information from the experience of others.

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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

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Simulations of bar populations b=6 time Beach visitors (a t ) n=4000 sites at the beach Bk=1000 b=6

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Simulations of bar populations b=6 time Beach visitors (a t ) n=4000 sites at the beach Bk=1000 b=8

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Simulations of bar populations b=6 time Beach visitors (a t ) n=4000 sites at the beach Bk=1000 b=20

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A derivation Interaction function The mean population on the next generation is given by where p k is the probability that k individuals choose a particular site. If p k is totally random (i.e. indiviudals are Poisson distributed) then

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b=6 a t+1 atat

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Simulations of bar populations b=6 time Beach visitors (a t ) n=4000 sites at the beach Bk=1000 b=6

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Simulations of bar populations b=6 time Beach visitors (a t ) n=4000 sites at the beach Bk=1000 b=8

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Simulations of bar populations b=6 time Beach visitors (a t ) n=4000 sites at the beach Bk=1000 b=20

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Period doubling route to chaos

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Are stock markets chaotic?

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Not really like the distributions we saw in lectue 1.

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El-Farol bar problem Arthur 1994

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El-Farol bar problem Arthur 1994

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El-Farol bar problem Arthur 1994

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Minority game Challet and Zhang 1997 Brain size is number of bits in signal (3)

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Minority game Challet and Zhang 1997

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Minority game Challet and Zhang 1998

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Break

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Do humans copy each other?

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Aschs experiment Asch (1955) Scientific American

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Aschs experiment Asch (1955) Scientific American

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Aschs experiment Asch (1955) Scientific American

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Milgrams experiment

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Hale (2008)

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Milgrams experiment Milgram & Toch (1969)

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

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Consequences of copying

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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.

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