Braess’ Paradox is a famous result in game theory which states that in a network where users selfishly seek to lower their travel times, the Nash equilibrium flows may increase after a new arc/road is added.
Braess’ Paradox can be demonstrated physically with springs, as seen in this nifty YouTube video:
When searching for information about Braess’ Paradox, I found a delightful post on Anna Nagurney’s blog.
In the basketball world, according to Bill Simmons of ESPN, there is the Ewing Theory. According to Simmons: The theory was created in the mid-’90s by Dave Cirilli, a friend of his who was convinced that Patrick Ewing’s teams (both at Georgetown and with New York) inexplicably played better when Ewing was either injured or missing extended stretches because of foul trouble. Simmons has a primer, Ewings Theory 101, which lists examples in basketball history where the removal of a top player (paradoxically) results in a better outcome for the basketball team.
Brian Skinner, a physicist at the University of Minnesota, wrote an article, “The Price of Anarchy in Basketball” in which he developed an analogy, through a model, between certain basketball plays and the Braess paradox, in order to further explore the Ewing Theory.
I’ve been enjoying the NBA basketball playoffs since my favorite team (the Chicago Bulls) won their first round series and beat the Miami Heat in the first game in the second round. The Bulls are without Derrick Rose, the best player on the Bulls. I hope there is not a “Derrick Rose Effect” that would cause the Bulls to be worse when he returns.
Are you aware of other interesting applications of Braess’ paradox?