Mechanism Design for Correlated Valuations: Efficient Methods for Revenue Maximization

Traditionally, much of the focus of the mechanism/auction design community has been on revenue optimal mechanisms for settings where bidders’ private valuations over outcomes can be reasonably thought of as independent of each other. This has been the case even though there is good reason to believe that valuations are often correlated and there are theoretical results suggesting that mechanisms designed with this correlation in mind can generate much higher revenue. In “Mechanism Design for Correlated Valuations: Efficient Methods for Revenue Maximization,” we look at the setting where there is correlation, but the exact distribution is unknown and must be estimated from samples. We show that in this setting, the previous extremely strong theoretical results around the usefulness of correlation are now very sensitive to the degree of correlation in the underlying distribution and the number of samples that the mechanism designer has access to. However, we also show that if correlation is sufficient, we can construct mechanisms, using a computationally efficient procedure, that significantly outperform traditional mechanism design paradigms.

[1]  Allard Beutel.  NASA Chooses American Companies to Transport U.S. Astronauts to Intern , 2015 .

[2]  Vincent Conitzer,et al.  Assessing the Robustness of Cremer-McLean with Automated Mechanism Design , 2015, AAAI.

[3]  Mehryar Mohri,et al.  Learning Algorithms for Second-Price Auctions with Reserve , 2016, J. Mach. Learn. Res..

[4]  Hamid Nazerzadeh,et al.  Dynamic Reserve Prices for Repeated Auctions: Learning from Bids , 2014, ArXiv.

[5]  Sergei Severinov,et al.  Individually rational, budget-balanced mechanisms and allocation of surplus , 2008, J. Econ. Theory.

[6]  D. Bergemann,et al.  Robust Mechanism Design , 2003 .

[7]  Tuomas Sandholm,et al.  Automated Design of Revenue-Maximizing Combinatorial Auctions , 2015, Oper. Res..

[8]  J. Harsanyi.  Games with Incomplete Information Played by “Bayesian” Players Part II. Bayesian Equilibrium Points , 1968 .

[9]  Vincent Conitzer,et al.  Automated Design of Robust Mechanisms , 2017, AAAI.

[10]  Harald Niederreiter,et al.  Probability and computing: randomized algorithms and probabilistic analysis , 2006, Math. Comput..

[11]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[12]  Tim Roughgarden,et al.  Simple versus optimal mechanisms , 2009, SECO.

[13]  Yishay Mansour,et al.  Learning Valuation Distributions from Partial Observation , 2014, AAAI.

[14]  Richard P. McLean,et al.  FULL EXTRACTION OF THE SURPLUS IN BAYESIAN AND DOMINANT STRATEGY AUCTIONS , 1988 .

[15]  Vincent Conitzer,et al.  Self-interested automated mechanism design and implications for optimal combinatorial auctions , 2004, EC '04.

[16]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[17]  Nima Haghpanah,et al.  Optimal auctions for correlated buyers with sampling , 2014, EC.

[18]  L. Khachiyan,et al.  The polynomial solvability of convex quadratic programming , 1980 .

[19]  Tim Roughgarden,et al.  Optimal and near-optimal mechanism design with interdependent values , 2013, EC '13.

[20]  Vincent Conitzer,et al.  Computationally Feasible Automated Mechanism Design: General Approach and Case Studies , 2010, AAAI.

[21]  D. H. Martin.  On the continuity of the maximum in parametric linear programming , 1975 .

[22]  Peter Stone,et al.  Adaptive Auction Mechanism Design and the Incorporation of Prior Knowledge , 2010, INFORMS J. Comput..

[23]  Vincent Conitzer,et al.  Maximizing Revenue with Limited Correlation: The Cost of Ex-Post Incentive Compatibility , 2016, AAAI.

[24]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[25]  Tim Roughgarden,et al.  On the Pseudo-Dimension of Nearly Optimal Auctions , 2015, NIPS.

[26]  Vincent Conitzer,et al.  Complexity of Mechanism Design , 2002, UAI.

[27]  Richard P. McLean,et al.  Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent , 1985 .

[28]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[29]  Dimitris Bertsimas,et al.  Robust game theory , 2006, Math. Program..

[30]  Giuseppe Lopomo.  Optimality and Robustness of the English Auction , 2001, Games Econ. Behav..

[31]  Jason D. Hartline.  Mechanism Design and Approximation , 2014 .

[32]  Mehryar Mohri,et al.  Optimal Regret Minimization in Posted-Price Auctions with Strategic Buyers , 2014, NIPS.

[33]  Chris Shannon,et al.  Uncertainty in Mechanism Design , 2021, 2108.12633.

[34]  P. Reny,et al.  Correlated Information and Mechanism Design , 1992 .

[35]  Ian A. Kash,et al.  General Truthfulness Characterizations Via Convex Analysis , 2012, WINE.

[36]  Vincent Conitzer,et al.  Mechanism Design with Unknown Correlated Distributions: Can We Learn Optimal Mechanisms? , 2017, AAMAS.

[37]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..