In the final scenes of “The Dark Knight” (spoiler alert!), the Joker gives the following choice to the passengers of two ferries: they can either blow up the other boat and save themselves, or themselves be blown up. If no one decides within a certain amount of time, both ferries are destroyed.
(...) This seminal problem in game theory has an important property: while cooperation is a more socially beneficial strategy, it is actually a more “stable” strategy for each person to betray the other, since this makes each better off independent of the whims of his friend. This behavior is known as a Nash equilibrium and is named after John Nash, well-known from the more obviously mathematical film, “A Beautiful Mind.”
Tuesday, September 22, 2009
Visually numbered
If you are a mathematician, how do you view some of the recent blockbusters of our time? Here's a window into one such mind:
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2 comments:
I am sure you got this from somewhere creditible but I remember Nash Equilibrium as - and I think I get this from a book I read abt Dr. Nash - Optimum result can be achieved by the group when each member of the group works in whats the best interest for the Group and Himself - "each strategy in a Nash equilibrium is a best response to all other strategies in that equilibrium". So in Case of "The Dark Knight" they reached Nash Equilibrium amongst themselves -- he he he ... The one you state more resembles "Adam Smiths Analogy" ...
P.S. this is my understanding of Nash Equilibrium.. not stated anywhere specifically.
Amit
According to wikipedia, Nash's equilibrium is:
Likewise, a group of players is in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others. However, Nash equilibrium does not necessarily mean the best cumulative payoff for all the players involved; in many cases all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium (e.g. competing businesses forming a cartel in order to increase their profits).
I am not well-versed enough to understand all this! But is sounds a lot like the choice that almost all of us make everyday in our lives!
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