Monday, 25 May 2015

Nash: Beautiful Mind, Baleful Consequences

It is really pleasing that Nash, the tortured genius, produced such staggering work in pure areas like geometry and PDEs, where he made astonishing advances that cannot be gainsaid.

Because his other, probably even more famous work - the Nash Equilibrium - was an 'advance' of a very dubious kind.

No problem with the maths (not that I am equipped to judge): as with so much in the pseudo-science of 'economics' it's the applications.  In the Real World - the one that matters - the simplifying assumptions behind so many theories just do not hold to the necessary degree for the edifices that are constructed on those foundations to be considered safe.  

No engineer would be permited to build a bridge on similarly flaky physical principles.  But pontificating economists and econometricians, wildly layering unjustified wobbly assumptions one upon another as though they were proper foundation-stones, infect the thought-processes of politicians and regulators.  Yes, and sometimes even businessmen, who can frequently be conned into paying tens of thouands for 'forecasts' that are quite literally not worth the paper they are printed on (as a glance at the disclaimers in 6-point at the bottom of the document make clear).

The Nash Equilibrium is mis-applied all over the place: within the models used to generate price forecasts - well, more fools the folk who buy them - but more seriously by regulators who reckon they can thereby 'understand' the markets they intervene in and supervise.   The flamboyant Taleb* rants against misuse of the Gaussian, but I'd say misuse of Nash is worse - not least, because it's generally less obvious; embedded deep, unacknowledged, its limitations less well know.  And idiot businessmen make speculative decisions that impact their shareholders; but idiot regulators make decisions that affect us all.

Nash's Nobel prize is therefore a rather depressing commentary on the ways of the world.  So much the better that he won the great maths prizes as well.

* Don't read Black Swan, he'd gone OTT by then - read Fooled By Randomness


dearieme said...

You mean he won the counterfeit Nobel Prize, Shirley?

Demetrius said...

On Friday 15th May, titled "Spending A Night Out" the picture of card players is in the very place were early researchers into game theory and mathematical economics were running poker schools. I was there. It explains why I have always had reservations about that field. I have a theory of my own which is that if you let Scottish bankers have the run of money creation you inevitably get major financial crashes.

andrew said...

nash - like you said - was one of the outstanding math brains of the 20th century.

he described an equilibrium (apologies for being boring and using wikipedia)
Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy. To see what this means, imagine that each player is told the strategies of the others. Suppose then that each player asks himself or herself: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?"

If any player could answer "Yes", then that set of strategies is not a Nash equilibrium. But if every player prefers not to switch (or is indifferent between switching and not) then the set of strategies is a Nash equilibrium. Thus, each strategy in a Nash equilibrium is a best response to all other strategies in that equilibrium

the thing is there is a bit of a collision with the real world

1 - Assumes you have full knowledge of everyone elses strategies

2 - Assumes you are a rational actor and actually want to maximise your benefit

Good for designing auctions/price discovery - especially if you are the seller / auctioneer
Both these assumptions are probably false for just about every purpose this tool is used for.

In fact some of the interesting work on ecomomics is how people are often not rational.

MyLateNightName said...

"infect the thought-processes of"

It is to this statement we should address most of our concerns; Power itself derives from it.

The real 'importance' of economics is to provide a body of authority - impenetrable to the man in the street - to which spurious appeals can be made when motives are questioned.
This is why such arcane terms and byzantine concepts are used.

Economics does not just seem to be wordy, vague bullshit full of numbers, graphs and non-sequitors, it is exactly that by design.

Here endeth the lesson etc...

Sebastian Weetabix said...

I agree the field is utter balls, but the presumption that our 'leaders' use this stuff to reach decisions is, IMHO, fanciful. Most are mildly sociopathic conventional plodders good at managing upwards who never threaten the status quo; that's why they get on (some of course are real psycho nut jobs with a patina of affable sociability). Once arrived, the biggest concern is to stay there and not have a serious fuck up on their watch. Change=risk... So those who question current assumptions and direction are, in most organisations, as welcome as a turd on the table. I find the idea of the average CEO or department head sitting down to puzzle things through with a bit of formal game theory a giggle.

The usual thinking process of one CEO I had the dreadful misfortune to work for was:
1. Did I think of it?
2. Does it contradict anything I've said before?
3. Will it benefit me personally?
4. If it goes wrong, what is my escape route and who will take the blame?
5. Is the person who came up with this a threat to my position?
6. Do the numbers all over again/change your assumptions/rinse and repeat anything up to 10 times to give the illusion of competence and control, by which time it is too late to put the scheme into effect and times have moved on.

In retrospect I was wrong to suggest his risk aversion and inability to take decisions was leading the organisation into ruinous stasis. I mean, I was absolutely right, but he didn't appreciate the insight, no matter how tactfully put, so he fired me 2 weeks before the board fired him. Damn!

Nick Drew said...

Andrew - some of the interesting work on ecomomics is how people are often not rational, yes and on this Taleb is quite good

'not rational' isn't quite correct, IMHO - it's 'have blind-spots', 'can't untuitively grasp', 'are easily distracted by ...', 'place even greater weight on ...' - that kind of real-world stuff

lateNite: 'by design' is a bit strong, but I'd agree those attributes are very useful for bedazzling people - rather like some theological constructs are

SW - that our 'leaders' use this stuff to reach decisions is fanciful: that's why I said 'infect', it is in the air, in the sneezes of people they encounter, and they breath it in and it attacks the brain

your checklist is excellent even if your delicacy as a courtier is not! You surely enjoy the account Hilary Mantell gives of Cromwell's astute manangement of Henry VIII

(we look forward to learning how she feels he ultimately slipped up in due course ...)

Sebastian Weetabix said...

Yes, I'm curious to read that too.... I read those books with a mixture of admiration and mounting annoyance. Cromwell seems to me a completely anachronistic 21st century figure and utterly at odds with contemporary accounts. Enjoyable nonetheless. I guess Mantel is motivated by her dislike of Catholicism; "it is not a religion for respectable people" - hah. I should bloody well hope not; that's what the CofE is for.

I fear an upbringing on the Clyde with a few years of University/Cranditz does not a courtier make. The veneer of civilisation is too thin. But I managed not to shout "make yer fucking mind up, ya witless bampot" at him. Perhaps I should have; the outcome would have been the same, but I would have enjoyed it.

Nick Drew said...

people have put to her that Cromwell = Campbell(A) but he seems to me more like a cross between Mandelson and Goodman(A)