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 don’t come back • Interaction function Schelling (1978) Micromotives and Macrobehaviour

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

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

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

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 pkis totally random (i.e. indiviudals are Poisson distributed) then

11. b=6 at+1 at

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

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

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

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. Asch’s experiment Asch (1955) Scientific American

27. Asch’s experiment Asch (1955) Scientific American

28. Asch’s experiment Asch (1955) Scientific American

29. Milgram’s experiment

30. Milgram’s experiment Hale (2008)

31. Milgram’s 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.