# John Nash Dissertation

But infrastructure after the catastrophe is constrained.

Or they might just flip a coin and easily coordinate on a single equilibrium.

They need a coordination mechanism of some sort, however.

To wit, each has the incentive to deviate from the conjectured brunette-brunette strategy combination to approach the blonde. Both has the incentive to deviate given the symmetry of the game, but we’re talking about one player at a time having the incentive to deviate from a brunette to the blonde given the conjecture that the other player is approaching a brunette.

There are three Nash equilibria to the same, two pure-strategy equilibria, and one mixed-strategy equilibrium.

Nash and all his friends prefer to pair with the blonde relative to the brunettes, but prefer to pair with one of the brunettes relative to not pairing up at all.

As Nash explains it, if all the men approach the blonde first, none of the men will pair off: The blonde will reject them all as a crowd, and her brunette friends will reject them all individually because none of the women will accept being second choice to her friend.If we consider the class of congestion game more broadly, again considering the case of aid agencies rushing to get assistance to a remote region, there are incentives for the aid agencies to coordinate in advance: for one agency to send in aid via the road, for the other agency to send in aid via the airport.But a distributive tension exists here as well, despite the altruistic aims of the agencies.First, note the strategy combination for the boys identified in the film — that both go for brunettes — is not an equilibrium.Each boy have the same incentive to deviate from going for a brunette given the conjecture that the other boy is going for a brunette.(Strategies in pure strategy equilibria are played with probability 1 or zero; strategies in mixed-strategy equilibria are played with probabilities less than one but greater than zero.) The two pure strategy equilibria are mirrors of each other.One of the boys pairs with the blonde, the other boy pairs with a brunette.But there is a distributive tension between the players.They might argue over which one of them ends up with the blonde and which “settles” for a brunette. Nash won the Nobel Memorial Prize in Economics in 1994 for his contributions to game theory. Still, as most adaptations do, the film differs from the book in several important ways.In the book, for example, Nash’s dissertation advisor tells him that his dissertation is trivial, which is a high insult in mathematics.

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