Article | Operations Research | January – February 2011

The Price of Fairness

by Dimitris Bertsimas, Vivek F. Farias and Nikolaos Trichakis


In this paper 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 focus on two well-accepted, axiomatically justified notions of fairness, viz., proportional fairness and max-min fairness. For these notions we provide a tight characterization of the price of fairness for a broad family of problems.

Keywords: Price; Fairness;


Bertsimas, Dimitris, Vivek F. Farias, and Nikolaos Trichakis. "The Price of Fairness." Operations Research 59, no. 1 (January–February 2011): 17–31.