Worst-case equilibria

Abstract

In a system where noncooperative agents share a common resource, we propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model where several agents share a very simple network leads to some interesting mathematics, results, and open problems. 2 2 The conference version of this work [Koutsoupias and Papadimitriou (1999) [17]] appeared a decade ago and it has been followed by a large amount of work on the concept of the price of anarchy (as witnessed by the extensive coverage in Nisan et al. (2007) [9]). In this journal version we tried to keep as much as possible the text of the original paper. There are, though, important changes because results that were substantially improved in the meantime are omitted. The other notable change is that here we use the term “price of anarchy” instead of the original term “coordination ratio”. The use of the latter term faded away in the literature, being replaced by the term “price of anarchy” which was first introduced in Papadimitriou (2001) [18].