The Price of Fairness

Abstract

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.

On the Efficiency-Fairness Trade-off

“…In particular, there has been a plethora of proposals in the literature under axiomatic bargaining, welfare economics, as well as in applications ranging from networks, air traffic management, healthcare and finance. We refer the reader to [19] and [4] for a more detailed exposition.…”

“…The impact of a higher value of α on the system efficiency has also received a lot of attention. In [4] the authors present tight upper bounds on the efficiency loss for the special cases of proportional and max-min fairness. For the more interesting general case of varying α (and thus giving the CDM the flexibility of the efficiency-fairness tradeoff), however, only empirical studies are available that suggest that a higher value of α results in higher efficiency loss, although counterexamples exist (see [18] and references therein).…”

“…The efficiency loss relative to the maximum system efficiency is the so called price of fairness [4], defined in this case…”

“…Also, in case of nonconvex utility sets, randomization over possible utility allocations results in a convex set (of expected utilities). For an extended discussion of Assumption 1 we refer the reader to [19] and [4].…”

An Incentive Compatible, Efficient Market for Air Traffic Flow Management

“…Indeed, [6] state that " ... While this work points at the possibility of dramatically reducing delay costs to the airline industry vis-a-vis current practice, the vast majority of these proposals remain unimplemented.…”