# s-game: equilibrium, a chimeric target

<< In 1950, John Nash — the mathematician later featured in the book and film “A Beautiful Mind” — wrote a two-page paper that transformed the theory of economics. His crucial, yet utterly simple, idea was that any competitive game has a notion of equilibrium: a collection of strategies, one for each player, such that no player can win more by unilaterally switching to a different strategy >>

<< Nash’s equilibrium concept, which earned him a Nobel Prize in economics in 1994, offers a unified framework for understanding strategic behavior not only in economics but also in psychology, evolutionary biology and a host of other fields. Its influence on economic theory “is comparable to that of the discovery of the DNA double helix in the biological sciences,” wrote Roger Myerson of the University of Chicago, another economics Nobelist >>

In a paper posted online last September AA << proved that no method of adapting strategies in response to previous games — no matter how commonsensical, creative or clever — will converge efficiently to even an approximate Nash equilibrium for every possible game. It’s “a very sweeping negative result,” Roughgarden (Tim Roughgarden) said >>

Erica Klarreich. In Game Theory, No Clear Path to Equilibrium. July 18, 2017.

https://www.quantamagazine.org/in-game-theory-no-clear-path-to-equilibrium-20170718/

Yakov Babichenko, Aviad Rubinstein. Communication complexity of approximate Nash equilibria. arXiv:1608.06580 Sep. 13,  2016

https://arxiv.org/abs/1608.06580