Posted ByDave Childs on April 06, 2002 at 10:25:29:
I finally saw "A beautiful Mind" the other day and was intrigued by the scene that explains the Nash Equilibrium. Remeber the blond in the bar scene.
Anyway, I started thinking about it and realized that using RPS as a model easily refutes the theory.
Here is my thinking: If the equlibrium states that players will do what is best considering the circumstances (ie they are better off going after the brunette rather than the blond).
In RPS
- best outcome is to win
- second best is to stalemate
- worst outcome is to lose
Therefore the Nash Equilibrium states that it would be in the best interest of all players to Stalemate.
Since this is obviously not the case with RPS the Nash Equilibrium is refuted!
QED