Bayesian algorithmic mechanism design

This article surveys recent work with an algorithmic flavor in Bayesian mechanism design. Bayesian mechanism design involves optimization in economic settings where the designer possesses some stochastic information about the input. Recent years have witnessed huge advances in our knowledge and understanding of algorithmic techniques for Bayesian mechanism design problems. These include, for example, revenue maximization in settings where buyers have multi-dimensional preferences, optimization of non-linear objectives such as makespan, and generic reductions from mechanism design to algorithm design. However, a number of tantalizing questions remain un-solved. This article is meant to serve as an introduction to Bayesian mechanism design for a novice, as well as a starting point for a broader literature search for an experienced researcher.

[1]  Christos H. Papadimitriou,et al.  On optimal single-item auctions , 2010, STOC '11.

[2]  S. Matthew Weinberg,et al.  Pricing randomized allocations , 2009, SODA '10.

[3]  Andrew Chi-Chih Yao,et al.  On revenue maximization for selling multiple independently distributed items , 2013, Proceedings of the National Academy of Sciences.

[4]  David C. Parkes,et al.  When Analysis Fails: Heuristic Mechanism Design via Self-correcting Procedures , 2009, SOFSEM.

[5]  David C. Parkes,et al.  Self-correcting sampling-based dynamic multi-unit auctions , 2009, EC '09.

[6]  Jessica Taylor.  Black-Box Reductions in Mechanism Design , 2014 .

[7]  Jason D. Hartline.  Bayesian Mechanism Design , 2013, Found. Trends Theor. Comput. Sci..

[8]  Renato Paes Leme,et al.  Optimal mechanisms for selling information , 2012, EC '12.

[9]  John Thanassoulis,et al.  Haggling over substitutes , 2004, J. Econ. Theory.

[10]  Arpita Ghosh,et al.  Optimal Contest Design for Simple Agents , 2016, TEAC.

[11]  Christos Tzamos,et al.  The Complexity of Optimal Mechanism Design , 2012, SODA.

[12]  B. Moldovanu,et al.  The Limits of ex post Implementation , 2006 .

[13]  Alejandro M. Manelli,et al.  Bundling as an optimal selling mechanism for a multiple-good monopolist , 2006, J. Econ. Theory.

[14]  Nima Haghpanah,et al.  Bayesian optimal auctions via multi- to single-agent reduction , 2012, EC '12.

[15]  Xiaohui Bei,et al.  Bayesian incentive compatibility via fractional assignments , 2010, SODA '11.

[16]  S. Matthew Weinberg,et al.  Matroid prophet inequalities , 2012, STOC '12.

[17]  Yang Cai,et al.  Understanding Incentives: Mechanism Design Becomes Algorithm Design , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[18]  Chaitanya Swamy,et al.  Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players , 2013, WINE.

[19]  Yang Cai,et al.  Optimal Multi-dimensional Mechanism Design: Reducing Revenue to Welfare Maximization , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[20]  Anna R. Karlin,et al.  Approximate revenue maximization in interdependent value settings , 2014, EC.

[21]  Patrick Briest,et al.  Uniform Budgets and the Envy-Free Pricing Problem , 2008, ICALP.

[22]  Noam Nisan,et al.  The menu-size complexity of auctions , 2013, EC '13.

[23]  Brendan Lucier,et al.  Bayesian algorithmic mechanism design , 2009, STOC '10.

[24]  Tim Roughgarden,et al.  Revenue maximization with a single sample , 2010, EC '10.

[25]  Robert B. Wilson.  Communications to the Editor---Competitive Bidding with Disparate Information , 1969 .

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

[27]  G. Pavlov,et al.  Optimal Mechanism for Selling Two Goods , 2011 .

[28]  Aaron Roth,et al.  Selling privacy at auction , 2010, EC '11.

[29]  J. Rochet,et al.  Ironing, Sweeping, and Multidimensional Screening , 1998 .

[30]  S. Matthew Weinberg,et al.  A Simple and Approximately Optimal Mechanism for an Additive Buyer , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[31]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[32]  Amin Saberi,et al.  On the hardness of optimal auctions , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[33]  Noam Nisan,et al.  On the Computational Power of Demand Queries , 2009, SIAM J. Comput..

[34]  Kamesh Munagala,et al.  Optimal auctions via the multiplicative weight method , 2012, EC '13.

[35]  Moshe Babaioff,et al.  Peaches, lemons, and cookies: designing auction markets with dispersed information , 2013, EC '13.

[36]  E. Samuel-Cahn.  Comparison of Threshold Stop Rules and Maximum for Independent Nonnegative Random Variables , 1984 .

[37]  Shuchi Chawla,et al.  Bayesian mechanism design for budget-constrained agents , 2011, EC '11.

[38]  Qiqi Yan,et al.  Mechanism design via correlation gap , 2010, SODA '11.

[39]  Moshe Tennenholtz,et al.  Signaling Schemes for Revenue Maximization , 2012, TEAC.

[40]  Shuchi Chawla,et al.  Algorithmic pricing via virtual valuations , 2007, EC '07.

[41]  Yang Cai,et al.  Simple and Nearly Optimal Multi-Item Auctions , 2012, SODA.

[42]  Amir Ronen,et al.  On approximating optimal auctions , 2001, EC '01.

[43]  Yang Cai,et al.  Reducing Revenue to Welfare Maximization: Approximation Algorithms and other Generalizations , 2013, SODA.

[44]  Mukund Sundararajan,et al.  Robust mechanisms for risk-averse sellers , 2010, EC '10.

[45]  Rahul Deb,et al.  Ironing in Dynamic Revenue Management: Posted Prices & Biased Auctions , 2013, SODA.

[46]  T. Roughgarden,et al.  Optimal and near-optimal mechanism design with interdependent values , 2013, EC '13.

[47]  S. Matthew Weinberg,et al.  Optimal and Efficient Parametric Auctions , 2013, SODA.

[48]  Itai Ashlagi,et al.  An optimal lower bound for anonymous scheduling mechanisms , 2009, EC '09.

[49]  Shuchi Chawla,et al.  Prior-independent mechanisms for scheduling , 2013, STOC '13.

[50]  Rudolf Müller,et al.  Optimal mechanism design for the private supply of a public good , 2013, Games Econ. Behav..

[51]  Éva Tardos,et al.  Information Asymmetries in Common-Value Auctions with Discrete Signals , 2013, EC.

[52]  Robert D. Kleinberg,et al.  Bayesian incentive compatibility via matchings , 2011, SODA '11.

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

[54]  Hu Fu,et al.  Prior-independent auctions for risk-averse agents , 2013, EC '13.

[55]  G. Pavlov,et al.  A Property of Solutions to Linear Monopoly Problems , 2011 .

[56]  Christos Tzamos,et al.  Optimal Pricing Is Hard , 2012, WINE.

[57]  J. Rochet.  A necessary and sufficient condition for rationalizability in a quasi-linear context , 1987 .

[58]  Yang Cai,et al.  Extreme-Value Theorems for Optimal Multidimensional Pricing , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[59]  Jeffrey C. Ely,et al.  Ex-Post Incentive Compatible Mechanism Design , 2002 .

[60]  Yang Cai,et al.  An algorithmic characterization of multi-dimensional mechanisms , 2011, STOC '12.

[61]  Sudipto Guha,et al.  Approximation Schemes for Sequential Posted Pricing in Multi-unit Auctions , 2010, WINE.

[62]  Farkas Lemma.  Reduced Form Auctions Revisited , 2003 .

[63]  Alejandro M. Manelli,et al.  Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly , 2004, J. Econ. Theory.

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

[65]  Jason D. Hartline,et al.  Multi-parameter mechanism design and sequential posted pricing , 2009, STOC '10.

[66]  Christos Tzamos,et al.  Mechanism design via optimal transport , 2013, EC '13.

[67]  E. Maasland,et al.  Auction Theory , 2021, Springer Texts in Business and Economics.

[68]  Shuchi Chawla,et al.  The power of randomness in bayesian optimal mechanism design , 2010, EC '10.

[69]  Shuchi Chawla,et al.  Multi-parameter mechanism design and sequential posted pricing , 2010, BQGT.

[70]  Xue Chen,et al.  On the Approximation Ratio of k-Lookahead Auction , 2011, WINE.

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

[72]  Tim Roughgarden,et al.  Supply-limiting mechanisms , 2012, EC '12.

[73]  S. Matthew Weinberg,et al.  Prophet Inequalities with Limited Information , 2013, SODA.

[74]  Vasilis Syrgkanis,et al.  Vickrey Auctions for Irregular Distributions , 2013, WINE.

[75]  Sanjeev Khanna,et al.  Mechanism Design for a Risk Averse Seller , 2012, WINE.

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

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

[78]  R. Brualdi.  Comments on bases in dependence structures , 1969, Bulletin of the Australian Mathematical Society.

[79]  Tim Roughgarden,et al.  Optimal mechanism design and money burning , 2008, STOC.

[80]  Saeed Alaei,et al.  Bayesian Combinatorial Auctions: Expanding Single Buyer Mechanisms to Many Buyers , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[81]  Nikhil R. Devanur,et al.  Prior-Independent Multi-parameter Mechanism Design , 2011, WINE.

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

[83]  Peter Bro Miltersen,et al.  Send mixed signals: earn more, work less , 2012, EC '12.

[84]  Robert B. Wilson.  Competitive Bidding with Disparate Information , 2007 .

[85]  R. Zeckhauser,et al.  Optimal Selling Strategies: When to Haggle, When to Hold Firm , 1983 .

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

[87]  George Pierrakos,et al.  Simple, Optimal and Efficient Auctions , 2011, WINE.

[88]  Xi Chen,et al.  The Complexity of Optimal Multidimensional Pricing , 2013, SODA.

[89]  Yeon-Koo Che,et al.  Generalized Reduced-Form Auctions: A Network-Flow Approach , 2013 .

[90]  Jeremy I. Bulow,et al.  The Simple Economics of Optimal Auctions , 1989, Journal of Political Economy.

[91]  S. Matthew Weinberg,et al.  Bayesian Truthful Mechanisms for Job Scheduling from Bi-criterion Approximation Algorithms , 2014, SODA.

[92]  Kim C. Border.  IMPLEMENTATION OF REDUCED FORM AUCTIONS: A GEOMETRIC APPROACH , 1991 .

[93]  Richard Cole,et al.  The sample complexity of revenue maximization , 2014, STOC.

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

[95]  Balasubramanian Sivan,et al.  Optimal Crowdsourcing Contests , 2011, Encyclopedia of Algorithms.

[96]  Gagan Goel,et al.  Budget constrained auctions with heterogeneous items , 2009, STOC '10.

[97]  Nicole Immorlica,et al.  Constrained Signaling in Auction Design , 2013, SODA.

[98]  Pingzhong Tang,et al.  Optimal mechanisms with simple menus , 2014, EC.

[99]  David C. Parkes,et al.  An Ironing-Based Approach to Adaptive Online Mechanism Design in Single-Valued Domains , 2007, AAAI.

[100]  N. Nisan.  Chapter 9 - Algorithmic Mechanism Design: Through the lens of Multiunit auctions , 2015 .

[101]  Jeremy I. Bulow,et al.  Auctions versus Negotiations , 1996 .

[102]  Shahar Dobzinski,et al.  Optimal auctions with correlated bidders are easy , 2010, STOC.

[103]  Yvonne Schuhmacher,et al.  Mechanism Design A Linear Programming Approach , 2016 .

[104]  Nima Haghpanah,et al.  The Simple Economics of Approximately Optimal Auctions , 2012, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[105]  Ron Lavi,et al.  Algorithmic Mechanism Design , 2008, Encyclopedia of Algorithms.

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