Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round

We show that algorithms that follow the relax-and-round paradigm translate approximation guarantees into Price of Anarchy guarantees, provided that the rounding is oblivious and the relaxation is smooth. We use this meta result to obtain simple, near-optimal mechanisms for a broad range of optimization problems such as combinatorial auctions, the maximum traveling salesman problem, and packing integer programs. In each case the resulting mechanism matches or beats the performance guarantees of known mechanisms.

[1]  Moshe Babaioff,et al.  Truthful mechanisms with implicit payment computation , 2010, EC '10.

[2]  Tim Roughgarden,et al.  Welfare guarantees for combinatorial auctions with item bidding , 2011, SODA '11.

[3]  Uriel Feige,et al.  On maximizing welfare when utility functions are subadditive , 2006, STOC '06.

[4]  Renato Paes Leme,et al.  On the efficiency of the walrasian mechanism , 2013, EC.

[5]  Nicole Immorlica,et al.  A Unifying Hierarchy of Valuations with Complements and Substitutes , 2014, AAAI.

[6]  Martin Hoefer,et al.  Truthfulness and Stochastic Dominance with Monetary Transfers , 2013, TEAC.

[7]  Berthold Vöcking,et al.  Online Mechanism Design (Randomized Rounding on the Fly) , 2012, ICALP.

[8]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[9]  Chaitanya Swamy,et al.  Truthful and near-optimal mechanism design via linear programming , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[10]  Tim Roughgarden,et al.  The price of anarchy in games of incomplete information , 2012, SECO.

[11]  Christos H. Papadimitriou,et al.  On the Hardness of Being Truthful , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[12]  Khaled M. Elbassioni,et al.  Simpler Approximation of the Maximum Asymmetric Traveling Salesman Problem , 2012, STACS.

[13]  Éva Tardos,et al.  Composable and efficient mechanisms , 2012, STOC '13.

[14]  Yang Cai,et al.  Simultaneous bayesian auctions and computational complexity , 2014, EC.

[15]  Laurence A. Wolsey,et al.  An Analysis of Approximations for Finding a Maximum Weight Hamiltonian Circuit , 1979, Oper. Res..

[16]  Daniel Lehmann,et al.  Combinatorial auctions with decreasing marginal utilities , 2001, EC '01.

[17]  Allan Borodin,et al.  Price of anarchy for greedy auctions , 2009, SODA '10.

[18]  Moshe Babaioff,et al.  Multi-parameter mechanisms with implicit payment computation , 2013, EC '13.

[19]  Jon M. Kleinberg,et al.  Approximation algorithms for disjoint paths problems , 1996 .

[20]  Tim Roughgarden,et al.  Barriers to Near-Optimal Equilibria , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[21]  Nicole Immorlica,et al.  On the limits of black-box reductions in mechanism design , 2012, STOC '12.

[22]  Robert D. Carr,et al.  Randomized metarounding , 2002, Random Struct. Algorithms.

[23]  Paul Dütting,et al.  Valuation Compressions in VCG-Based Combinatorial Auctions , 2013, WINE.

[24]  Aravind Srinivasan,et al.  On k-Column Sparse Packing Programs , 2009, IPCO.

[25]  Annamária Kovács,et al.  Bayesian Combinatorial Auctions , 2008, ICALP.

[26]  Renato Paes Leme,et al.  On the efficiency of equilibria in generalized second price auctions , 2011, EC '11.

[27]  Michal Feldman,et al.  Simultaneous auctions are (almost) efficient , 2012, STOC '13.

[28]  Tim Roughgarden,et al.  Black-Box Randomized Reductions in Algorithmic Mechanism Design , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[29]  Prabhakar Raghavan,et al.  Randomized rounding: A technique for provably good algorithms and algorithmic proofs , 1985, Comb..

[30]  A. Frank.  Connections in Combinatorial Optimization , 2011 .

[31]  Paul Dütting,et al.  Algorithms against Anarchy: Understanding Non-Truthful Mechanisms , 2015, EC.

[32]  Tim Roughgarden,et al.  From convex optimization to randomized mechanisms: toward optimal combinatorial auctions , 2011, STOC '11.

[33]  Berthold Vöcking,et al.  Approximation techniques for utilitarian mechanism design , 2005, STOC '05.

[34]  Moshe Lewenstein,et al.  Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs , 2005, JACM.