We study resource allocation problems that involve multiple self-interested parties or players, and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a``fair'' allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We provide a tight characterization for the price of fairness for a general class of fair allocations that includes  proportional (Nash) fairness and max-min fairness. We further discuss applications of our results  in a variety of real world settings: communication networks, airtransportation and organ transplantation.

(joint work with Vivek Farias and Nikos Trichakis, MIT)