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Tuesday, April 03, 2018

Always Out of Balance: Looking for Equilibria

Nicepiece, which includes a short, easy to understand video  that explains the basics of the Nash Equilibrium.  We sought to use these methods to understand competitive behavior.   Not very successfully I admit, but the approach did make us think of better models for the processes and integrated behaviors involved.  Even the supposed rationality of decisions were an issue.  It is what we called competitive modeled economics. What were the right counter behavior for competition?

Always Out of Balance  By Neil Savage  in  
Communications of the ACM, Vol. 61 No. 4, Pages 12-14

"Computational Theorists show that there is no easy way to to find Nash Equilibria, so game theory will have to look in new directions"....

When John Nash won the Nobel Prize in economics in 1994 for his contribution to game theory, it was for an elegant theorem. Nash had shown that in any situation where two or more people were competing, there would always be an equilibrium state in which no player could do better than he was already doing. That theorem has since been used to model all sorts of competitive systems, from markets to nuclear strategy to living creatures competing for finite resources.

"In some sense, it started not just game theory, but also modern economics," says Christos Papadimitriou, a professor of computer science at Columbia University. Nash's idea gave economists the ability to create hypotheses about market design, for instance. They could now ask what happened when a market reached equilibrium.

Nash's theorem is also an essential component of game theory, which had first been developed by computing pioneer John von Neumann. "Games are a mathematical thought experiment and we study them just because we want to understand how strategic rational players would behave in situations of conflict," Papadimitriou says. "And that's important because all of society is full of such situations."

Though Nash proved that at least one such Nash equilibrium existed for all games, what he did not do was predict how an equilibrium might be reached in a given situation. Was there, scientists wanted to know, an algorithm that would show players how to efficiently reach an equilibrium? After more than 65 years of researchers' studying that question, the answer turns out to be no, there is not. That means economists had better start rethinking some of their models. .... "

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