Wednesday, November 16, 2005

John Nash and Adam Smith

An unsigned piece in The Republican: “Old adages fail in handicapping ‘new’ NFL” makes a tail-end reference to a movie that in turn has a script writer having the main character mouthing something alleged to have been said by John F. Nash, the mathematical genius who, among many other claims to fame, provided a mathematical solution to the “Bargaining Problem” (Econometrica, vols. XVIII, 1950 and XXI, 1953):

“I think back to a line uttered by Russell Crowe, playing mathematician John Nash in the movie "A Beautiful Mind" - "Adam Smith needs revision." Translated, it's time for new thinking to replace conventional wisdom. Now more than ever, you must think outside the box to win.”

As you may know, my other academic interest beside Adam Smith is in the science and practice of negotiation. I have spent 33 years researching, writing, teaching and consulting in bargaining behaviours, and, of course, I am familiar with John Nash’s work in this area (it features in my MBA elective course in Negotiation and is regularly visited by students in their examinations).

When I saw the film, “Beautiful Minds”, I enjoyed it, except for the references to Adam Smith. I am not at all sure of the authenticity of this attributed statement (I know that much of the portrayal of Nash was ‘economical’ with the truth – but it is a good movie nevertheless), and if it is true it must have followed from a misunderstanding by Nash of Smith’s philosophy.

The Nash ‘idealised’ solution to the Bargaining Problem is about the properties of a solution and not about the processes by which solutions to real world bargaining problems are found.

The assumptions of his solution model impose strict conditions: the two bargainers are ‘highly rational’; that ‘each can compare his desires various things’; ‘they are equal in bargaining skill; and that ‘each has full knowledge for the tastes and preferences of the other’. From these assumptions, a mathematical relationship (using ‘numerical utility’ theory) is built based on the ‘desire of each individual to maximise his gain in bargaining’.
The bargaining solution is the one that maximises the product of the net gains in utility to each individual for their bargaining.

If we take Adam Smith’s supposed assumption of utility maximising individuals (this is the version promoted by the University of Chicago and generally accepted across US campuses populated by mathematical economists) it is difficult to see how ‘Chicago’ economists would be different from ‘Nash’ economists.

It might be that Adam Smith could be considered different; he studied the process of ‘truck, barter and exchange’ and showed how two individuals, to achieve their own self-interests in the outcome would do so by serving the self-interests of the other party and not just their own – if they considered only their own they would deadlock. But Smith was not measuring the optimum outcome, nor specifying assumptions that imply what that outcome would be.
The Nash solution (especially in his second 1953 article) requires co-operation to achieve the optimum solution because all sub-optimal solutions leaves one or both bargainers worse off. Their maximisation desires force them to co-operate.

I conclude that the script writer was wrong: Adam Smith does not need revision, at least on this matter.

Incidentally, when Rand economists in 1952 made their discoveries associated with the Prisoner’s Dilemma game, showing that the majority of players did not find the ‘co-operative solution’ (in my experiments with managers in the 1970s-80s, only 8 per cent of pairs played ‘co-operate-co-operate’, the rest, 92 per cent, played ‘defection’) they wrote to John Nash asking him to comment, given this outcome and they suggested that the Nash solution was not the common solution. He did not reply. Maybe Nash needs revision if his solution is treated other than as an ideal?


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