Saw A Beautiful Mind today and quite enjoyed it. I was worried Nash's career would be butchered and his work made out to be codebreaking, so that it might be made into something saleable for the great unwashed. I will only say I was relieved and impressed by the role that his codebreaking was purported to play in the larger scheme of his career.
Opie managed to maintain dramatic heft and pathos while staying surprisingly true to Nash's life and the nature of his work. He also employed some cinematic devices that I found quite clever, but that may only be because I am a movie cretin.
Anyway, while the movie was certainly not about the content of Nash's work and not a timeline of his career (and shouldn't be), it did manage to convey a reasonably true sense of both, as far as I know. Nash's surprise at the range of applications of Nash equilibrium was an especially nice touch.
The only major problem really was that Nash's analysis for his buddies of the game of picking up dames in a bar was wrong. The game Nash described has no pure strategy equilibrium but only mixed ones -- in equilibrium each guy randomizes over the potential mates to shoot for, because if all went for someone besides the hot blonde, someone could deviate and pick her off for sure. In fact the real Nash's major contribution revolved around exactly that sort of randomization -- once you allow for it and define the notion of equilibrium as mutual optimization, proving the existence of equilibrium in a large class of games (which Nash did) is trivial.
(Well, I guess that's not a major problem because it's hard to do a mixed equilibrium properly in a movie. But don't think it's some super clever trick to explain what Nash equilibrium is all about. It goes through one iteration of best replies and stops. But it does capture the idea of a best reply by one player to the strategies of other players.)
Small nitpick i: the reception for the equilibrium concept at Princeton was very warm in the movie. In fact at the time the reception was mixed. John von Neumann, the father of game theory, considered it an unprofound cross between von Neumann's work and a basic fixed point theorem.
Small nitpick ii: the Nobel Prize committee guy declares that Nash's analysis of the bargaining problem had applications to auction design & antitrust cases. That of course is false; the bargaining problem was an application of cooperative game theory, which has nothing to do with auction theory or the industrial organization theory behind antitrust analysis in economics. Nash's work on the bagaining problem was I believe mentioned in the Nobel Prize citation, but is not the reason he won the prize - he won for equilibrium in non-cooperative games.
Thoughtful
LordoftheRings
Lord of the Rings
December 31, 2001
Hubby and I saw lord of the rings this weekend and really enjoyed it. Only problem for me was not enough "breathing room". Every time an evil was fought and won another one came down the pike. Has oscar written all over it. Scenery exquisite. Time to head to New Zealand.
