Writers Compete to Bag the Nash Equilibrium
The Nash equilibrium is really not as complex as Bart Kosko makes it sound (Commentary, Feb. 13). Imagine a number of stores, all selling a particular brand of computer. Some of the stores provide lots of hand-holding and personal support; some are discounters; some are in between. Each has found a market niche in which to succeed. Naturally, the prices at which these stores sell their computers vary, although each charges the maximum it has found to be successful. That is a Nash equilibrium.
No store can raise its price, since it has already discovered that raising the price will drive away customers and reduce profits. No store will lower its price, since it has found that doing so will not attract enough new customers to make the reduction worthwhile. No store will add or remove services, since that will reduce profits or drive away core customers. Each store has optimized its strategy with respect to the other stores and to the customers who make up the overall market. They are in equilibrium, and nothing any store can do on its own can improve its situation.
The only way things can change is if some external event modifies the world in which they are all living. The computer manufacturer may change its prices drastically, or it may make its computers so easy to use that no one needs extra personal attention. When something like that happens, the stores have to rethink their strategies. Eventually, another equilibrium will develop, and the situation will remain stable until some new external event triggers another change.
Russ Abbott
Professor, Computer Science
Cal State L.A.
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Kosko misuses an analogy to explain John Nash’s groundbreaking theory. He compares two competitive situations: children competing for a hundred-dollar bill amid less-desirable pennies and men competing for the most desirable woman (a blond) amid less desirable women (the brunets). The Nash equilibrium would lead the men to avoid competition by skipping the blond and winning favor with her usually ignored sidekicks. If they all went for the blond, at most one, and likely none, would be successful and no fallback position would exist with the irritated brunets. All risk ending up with nothing, so the choice is clear.
In the children’s example, obtaining the hundred-dollar bill is achievable. After one child gets the hundred, a fallback position remains and the other children revert to grabbing pennies. Unlike the ego-bruised brunets, the pennies would be collected with ease and everyone would end up with something, clearly a better choice for all.
Brendan Morrissey
Manhattan Beach
