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
Assorted on India
12 years ago
1 comment:
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
Post a Comment