Friday, October 12, 2007

Watch A Beautiful Mind on You Tube

A Beautiful Mind- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

What's your favorite scene from the film?

For Discussion: What's wrong with the following scene?

Nash's Theorem;
A theorem in game theory which guarantees the existence of a set of mixed strategies for finite, noncooperative games of two or more players in which no player can improve his payoff by unilaterally changing strategy

1 comment:

Anonymous said...

The Noncooperative Game in A Beautiful Mind
The movie suggests that a motivating example for the discovery of Nash equilibria might have been the strategies of five suitors most attracted to the same woman in a group of five. As suggested by the movie's visuals, positive outcomes occur only when each woman is approached by one suitor. In the two-person version of this game, each of two suitors, say John and Martin, decides with what probability, say x and y respectively, he will approach the more attractive of two women. The expected payoff to John is xa(1 – y) + (1 – x)by, where a > b > 0 since John prefers the more attractive woman. Likewise the expected payoff to Martin is (1 – x)cy + xd(1 – y), where c > d > 0. Two Nash equilibria for this game, as suggested in the movie, occur when x = 1 and y = 0 (with payoffs a and d) or when x = 0 and y = 1 (with payoffs b and c). The only other Nash equilibrium is when x = c/(c + d) and y = a/(a + b) (with payoffs ba/(a + b) < b and dc/(c + d) < d). At a Nash equilibrium, neither player can improve his expected payoff by unilaterally changing his strategy. Visit Maths Illustrated for a complete explanation of a similar example and of the wit in John's courtship line "I believe in assigning value to things."
http://www.haverford.edu/math/lbutler/review.html#sidebar