Nash Equilibrium

[koan]

I brought up John Nash in the "Fair Share" thread and seemed to kill it. Instead of pressing on, I decided that Nash deserved his own thread. I, like many others, am mostly aware of Nash because of the film "A Beautiful Mind". In fact, in my economics classes his name never arose. (And I'm young enough that it should have). I decided to look into his Equilibrium theory, the one that graduated him from Princeton and won him the Nobel, and try to find a primer or "layman's" description. I hope others will join me on the search. Or enlighten us if they already possess such information.

As a start:

The Wikipedia article on the Nash Equilibrium puts it pretty well:

"In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only their own strategy. If each player has chosen a strategy and no player can benefit by changing their strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium."

http://en.wikipedia.org...

Unfortunately, MW, that may be about as close to layman's terms as it can get. Game theory--and I don't claim to be anything other than a layman myself--is used to describe much more than just games. It applies to the study of economics, politics, international relations, any situation where two or more entities have interests which are opposing or conflicting. The description of each "player's" possible strategy in either terms of getting everything he wants, losing it all, or splitting some less-than-complete benefit with his opponents; and the mathematical analysis of the probablilities of each, can get quite complicated.

In my understanding, then, the Nash Equilibrium exists when, by this mathematical analyisis, no player, simply by changing his strategy, can gain an advantage which will pressure any other player to change his strategy. It doesn't factor in the possibility of negotiation, appealing to one's goodwill, or other intangibles. The old Cold War theory of Mutual Assured Destruction may have been one of those cases.

from answerbag

[koan]

The Nobel site has a good article in its press release section.

In his dissertation, Nash introduced the distinction between cooperative and non-cooperative games. His most important contribution to the theory of non-cooperative games was to formulate a universal solution concept with an arbitrary number of players and arbitrary preferences, i.e., not solely for two-person zero-sum games.

A "zero-sum game" means the gain to one side equals the loss to the other side or, with multiple players, the total gain equals the total loss.