Are Markets Rational or Irrational? The El Farol Problem Inductive reasoning Bounded rationality W Brian Arthur.

Are Markets Rational or Irrational?

• The El Farol Problem

• Inductive reasoning

• Bounded rationality

• W Brian Arthur

Traditional Economic Dogma• Belief: Problems have rational solution

– Newtonian mechanics for particle– Decide to get up when sun rises

• I can set a schedule

– Noughts and crosses• By moving first, can avoid defeat• If have to move second, can force draw

– BUT……– Chess

• More complex• Cannot predict moves of opponent

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Breakdown of perfect rationalityRationality of BOUNDED

How do we deal with such complex problems?

• Psychology teaches us– Moderately good at deductive logic– SUPERB at matching patterns

• Evolutionary benefit?

• Human behaviour– Act on deductions based on hypothesis– Discard hypothesis on failure– Seek new hypothesis– Strengthen/ improve successful hypothesis

To deal with complexity, we construct simple models that we CAN cope with

SCIENCE

Modelling Induction• Set up collection of ‘agents’

– Each forms set of beliefs (mental models)– Keep track of performance– At decision time, act on most credible model– Learn which work– Discard poor ones (possible time lag/ memory)

• WORLD OF TEMPORARY FULFILLED EXPECTATIONS– Evolutionary activity

– Origin of beliefs or consciousness?– Deep psychological questions..

Bounded Rationality and Minority Games – The ‘El Farol’ problem

• N>60 too crowded– Stay at home

• N<60 good time– Go to bar

What is the dynamics of attendance?• No obvious way to forecast

attendance • No rational deductive solution• Require inductive solution• No commonality of expectations• If all believe only a few will go,

all will go• If all believe most will go,

nobody goes• Expectations differ

Dynamic model• Recent attendance

– 44, 78, 56, 15, 23, 67, 84, 34, 45, 76, 40, 56, 22, 35, ?

• Predictors / hypotheses– Value previous week: 35– Average of previous 4 weeks

(40+56+22+35)/4=49– Trend over previous 8 weeks 29– Value 2 weeks ago 22– Value 5 weeks ago 76– Sum of 10 random numbers {1,9}

Process

Take decision

Check reliability of predictors

Add to, discard or modify predictors

New prediction

Set of predictors determines attendanceAttendance history determines active set of predictors

Active set forms an ecology

Fat tails & clustered volatility

Minority Game web page

• www.unifr.ch/econophysics/minority/– GET FOLDER

Parondo’s paradox – good news for losers

• Two games guaranteed to give steady string of losses generate winning streak if played alternately

Harmer & Abbott Nature 402 (1999) 864

• Game A: loaded coin toss

• B: Two coins – one of which is biased.– Which coin is tossed depends on how much

money player has– Game set so that ‘loaded’ coin is tossed more

often so player loses out in long term

• Played separately player steadily loses• Played alternately (Eg 2*A; 2*B)

– Capital steadily increases!!!– Also true if games are switched at random

A+B

A

B

time

capital

0

How can this be possible? Hypothesis:

• Switching creates a ratchet-like accumulation of wins

• Winning rounds, mainly due to good coin in B, carry winnings uphill

• Swapping ‘traps’ winnings before subsequent repetitions of same game introduce subsequent decline

May operate in economics and social dynamics to extract benefits from ostensibly detrimental situations eg declines in either birth rate or death rate together might combine with favourable consequencesCould be expensive to test in a casino!