Monday, May 25, 2015

Gnash Equilibrium

Philip Mirowski, Machine Dreams
The mathematical price of demonstrating that every game had a fixed value was the unloading of all analytical ambiguity onto the very definition of the game. Far from being daunted at a game without determinate bounds, Nash was already quite prepared to relinquish any fetters upon the a priori specification of the structure of the game, given that the entire action was already confined within the consciousness of the isolated strategic thinker. The game becomes whatever you think it is. He dispensed with dummies, exiled the automata, and rendered the opponent superfluous. This was solipsism with a vengeance.
Yanis Varoufakis, "The Dance of the Meta-Axioms":
In game theory itself, questions were raised about the plausibility of presuming that rational agents must always select behaviour consistent with Nash’s (1951) equilibrium. In the context of static games it became apparent that disequilibrium behaviour could be fully rationalised and rendered consistent with infinite order common knowledge rationality. Similarly, it transpired that out-of-equilibrium behaviour could be just as rational in finite dynamic games as the equilibrium path proposed by Nash and his disciples.  As for indefinite horizon games, the devastating force of indeterminacy was felt in the form of the so-called Folk Theorem which shows that, in interactions that last for an unspecified period, anything goes. And yet, all applications of game theory, from theories of Central Bank behaviour to industrial organisation, labour economics and voting models, ignore these challenges, assuming that behaviour will remain on the equilibrium path.

1 comment: said...

Yeah, and Phil went even further and said that it was Nash showing his paranoid shizophrenia. I have told Phil personally that this was over the top and overdoing it, even if Nash freaked out when Dresher and Flood did their repeated Prisoner's Dilemma experiments and even laissez faire economist Armen Alchian started cooperating after awhile.

There has long been a big debate between the pro-Nasha and pro-von Neumann crowds, with Sylvia Nasar mouthpiecing for the pro-Nash crowd and Phil speaking for the pro-von Neumann crowd. I like Phil's emphasis on the computational side of von Neumann at the end, but one who was so into worrying about cold war influences on economics should have kept in mind that it was the pro-cooperative game theoretic equilibrium von Neumann who wanted to nuke the Soviets ASAP and had top US military officers hovering over his stomach cancer deathbed to retrieve his last utterances about military strategy.

OTOH, nobody knows what went on the one apparently hostile conversation Nash and von Neumann had, with differing accounts reported by their respective supporters. Some years ago I had to make an author remove a footnote from a paper that claimed a particular version of it by pointing out that a) only the two them were present, and b) one was dead and the other was crazy. And now the crazy one is also dead.