Butterworth and Braess
In this article, Guardian contributor Jon Butterworth ponders the usefulness of applying Game Theory principles to two different decisions: Where to send his child to school, and what the eventual future of particle physics in Europe will be. Each of these decisions involves a different set of players independently making decisions to serve their own self interest: parents must decide where to send their children to school and particle physicists in Europe must decide where to work.
The implications of the Nash equilibrium are immediately apparent. The strict best response by any parent or particle physicist will be in reaction to the dominant strategy of society. If there is a new particle accelerator and many scientists of international acclaim are drawn there due to any number of factors (pay, promising breakthroughs) then the strict best response of a European particle physicist will be to apply for a job there. If there is a school in England, where Mr. Butterworth lives, that is attended by the children of scientists, and is popular in the scientific community, it may be a best response for Mr. Butterworth to send his son there. In both cases, a dominant strategy and a strict best response form a Nash equilibrium for the given situation.
Mr. Butterworth then brings up the idea of Braess’ paradox, which says that many times smart individual decisions can be counter-productive to the progress of the whole. For example, if a certain particle physics project was joined by a large number of highly intelligent and internationally respected researchers, then the goals of the project may become clouded or confused amongst the individual aspirations of the team members. It might in this case be more simple for these scientists to be working on multiple projects. By the same token, if one school in England is bombarded by applications and puts all sorts of influential and motivated people on its board, there may be conflicting visions about the particulars of education. Perhaps there is an ideal division of resources in each case, multiple Nash equilibriums, that can be formed which would increase the quality of schools and scientific research institutes. Food for thought.