Interpolating Between Truthful and non-Truthful Mechanisms for Combinatorial Auctions

We study the communication complexity of combinatorial auctions via interpolation mechanisms that interpolate between non-truthful and truthful protocols. Specifically an interpolation mechanism has two phases. In the first phase, the bidders participate in some non-truthful protocol whose output is itself a truthful protocol. In the second phase, the bidders participate in the truthful protocol selected during phase one. Note that virtually all existing auctions have either a non-existent first phase (and are therefore truthful mechanisms), or a non-existent second phase (and are therefore just traditional protocols, analyzed via the Price of Anarchy/Stability). The goal of this paper is to understand the benefits of interpolation mechanisms versus truthful mechanisms or traditional protocols, and develop the necessary tools to formally study them. Interestingly, we exhibit settings where interpolation mechanisms greatly outperform the optimal traditional and truthful protocols. Yet, we also exhibit settings where interpolation mechanisms are provably no better than truthful ones. Finally, we apply our new machinery to prove that the recent single-bid mechanism of Devanur et. al. [DMSW15] (the only pre-existing interpolation mechanism in the literature) achieves the optimal price of anarchy among a wide class of protocols, a claim that simply can't be addressed by appealing just to machinery from communication complexity or the study of truthful mechanisms.

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

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

[3]  Paul Dütting,et al.  Simplicity-expressiveness tradeoffs in mechanism design , 2011, EC '11.

[4]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[5]  Elchanan Mossel,et al.  Inapproximability for VCG-based combinatorial auctions , 2010, SODA '10.

[6]  Shahar Dobzinski,et al.  On the Complexity of Computing an Equilibrium in Combinatorial Auctions , 2014, SODA.

[7]  Noam Nisan,et al.  Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders , 2009 .

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

[9]  R. Vohra,et al.  Calibrated Learning and Correlated Equilibrium , 1996 .

[10]  Paul Dütting,et al.  Expressiveness and robustness of first-price position auctions , 2013, EC.

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

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

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

[14]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[15]  Jason D. Hartline,et al.  Price of anarchy for auction revenue , 2014, EC.

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

[17]  Renato Paes Leme,et al.  Sequential auctions and externalities , 2011, SODA.

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

[19]  S. Hart,et al.  A simple adaptive procedure leading to correlated equilibrium , 2000 .

[20]  Éva Tardos,et al.  Bayesian sequential auctions , 2012, EC '12.

[21]  Theodore Groves,et al.  Incentives in Teams , 1973 .

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

[23]  Shahar Dobzinski,et al.  Two Randomized Mechanisms for Combinatorial Auctions , 2007, APPROX-RANDOM.

[24]  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).

[25]  Gagan Goel,et al.  Clinching auctions beyond hard budget constraints , 2014, EC.

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

[27]  Gal Shahaf,et al.  Inapproximability of Truthful Mechanisms via Generalizations of the VC Dimension , 2014, STOC.

[28]  Noam Nisan,et al.  Truthful randomized mechanisms for combinatorial auctions , 2012, J. Comput. Syst. Sci..

[29]  Nikhil R. Devanur,et al.  Simple Auctions with Simple Strategies , 2015, EC.

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

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

[32]  Shahar Dobzinski,et al.  The computational complexity of truthfulness in combinatorial auctions , 2012, EC '12.

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