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 Increasing complexity Breakdown of perfect rationality Rationality 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 ( )/4=49 –Trend over previous 8 weeks29 –Value 2 weeks ago22 –Value 5 weeks ago76 –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 attendance Attendance history determines active set of predictors Active set forms an ecology

Fat tails & clustered volatility

Minority Game web page –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 consequences Could be expensive to test in a casino!