Price of Fairness for allocating a bounded resource

We study the problem faced by a decision maker who wants to allocate a scarce resource among several agents in order to maximize the total utility. An optimal solution may present a very unbalanced allocation of the resource to the agents and hence be perceived as unfair. On the other hand balanced allocations may be far from the optimum. In this paper we are interested in assessing the quality of fair solutions, i.e., in measuring the system efficiency loss under a fair allocation compared to the one that maximizes the total utility. This indicator is called the Price of Fairness and we study it under three different definitions of fairness, namely maximin, Kalai–Smorodinski and proportional fairness.

[1]  Ulrich Pferschy,et al.  The Subset Sum game☆ , 2014, Eur. J. Oper. Res..

[2]  Ioannis Caragiannis,et al.  The Efficiency of Fair Division , 2009, Theory of Computing Systems.

[3]  Ariel D. Procaccia,et al.  Beyond Dominant Resource Fairness , 2015, ACM Trans. Economics and Comput..

[4]  Benjamin Hindman,et al.  Dominant Resource Fairness: Fair Allocation of Multiple Resource Types , 2011, NSDI.

[5]  Emanuel Melachrinoudis,et al.  The linear multiple choice knapsack problem with equity constraints , 2005 .

[6]  Gerhard Fettweis,et al.  Robust Rate Adaptation and Proportional Fair Scheduling With Imperfect CSI , 2015, IEEE Transactions on Wireless Communications.

[7]  Mhand Hifi,et al.  An exact algorithm for the knapsack sharing problem , 2005, Comput. Oper. Res..

[8]  Maurizio Naldi,et al.  Maximin Fairness in Project Budget Allocation , 2016, Electron. Notes Discret. Math..

[9]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[10]  Steven J. Brams,et al.  Fair division - from cake-cutting to dispute resolution , 1998 .

[11]  Gagan Goel,et al.  Single-Parameter Combinatorial Auctions with Partially Public Valuations , 2010, SAGT.

[12]  Alec Morton,et al.  Inequity averse optimization in operational research , 2015, Eur. J. Oper. Res..

[13]  Yonatan Aumann,et al.  The Efficiency of Fair Division with Connected Pieces , 2010, WINE.

[14]  Dimitris Bertsimas,et al.  On the Efficiency-Fairness Trade-off , 2012, Manag. Sci..

[15]  Lei Wu,et al.  An exact decomposition algorithm for the generalized knapsack sharing problem , 2016, Eur. J. Oper. Res..

[16]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[17]  Steven J. Brams.  Fair Division* , 2009, Encyclopedia of Complexity and Systems Science.

[18]  Deeparnab Chakrabarty,et al.  Knapsack Problems , 2008 .

[19]  C ParkesDavid,et al.  Beyond Dominant Resource Fairness , 2015 .

[20]  Alexander Skopalik,et al.  Budget-Restricted Utility Games with Ordered Strategic Decisions , 2014, SAGT.

[21]  M Butler,et al.  Fairness versus efficiency in charging for the use of common facilities , 2002, J. Oper. Res. Soc..

[22]  George Kozanidis,et al.  Solving the linear multiple choice knapsack problem with two objectives: profit and equity , 2009, Comput. Optim. Appl..

[23]  Mario Köppen,et al.  Meta-heuristic approach to proportional fairness , 2012, Evolutionary Intelligence.

[24]  D. Marc Kilgour,et al.  Handbook of Group Decision and Negotiation , 2014, Advances in Group Decision and Negotiation.

[25]  Edward G. Coffman,et al.  Approximation algorithms for bin packing: a survey , 1996 .

[26]  Andrea Pacifici,et al.  Brief Announcement: On the Fair Subset Sum Problem , 2015, SAGT.

[27]  Julie A. Shah,et al.  On Fairness in Decision-Making under Uncertainty: Definitions, Computation, and Comparison , 2015, AAAI.

[28]  E. Kalai,et al.  OTHER SOLUTIONS TO NASH'S BARGAINING PROBLEM , 1975 .

[29]  Masako Fujimoto,et al.  An exact algorithm for the knapsack sharing problem with common items , 2006, Eur. J. Oper. Res..

[30]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[31]  Dan W. Brockt,et al.  The Theory of Justice , 2017 .

[32]  Dimitris Bertsimas,et al.  The Price of Fairness , 2011, Oper. Res..