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Monday, January 17, 2011

Computability of Nash Equilibria...

An excellent post on the computability of Nash equilibria of normal form games. I quote:
"Bottom line: Rational players can reason about and make use of Nash’s rational prediction, but they cannot deduce it. The prediction should somehow magically pop up in their minds."
I particularly like the author's reference to a paragraph of John Nash's doctoral thesis that hints at the issue.  Apparently this paragraph never made it into the published version of the thesis.  Here is a Google Scholar link to a bunch of other papers on the subject...

Why should we care about the computability of Nash equilibria? If agents are not able to deduce the Nash equilibria from the payoff matrix, then this cripples game theory as a predictive model of human behaviour (except in the subset of normal form games that are simplistic enough that the Nash equilibrium can be deduced from the payoff matrix by the agents).  The question then becomes: How well do simplistic normal form games map to real world decisions?

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