A Simple and Approximately Optimal Mechanism for an Additive Buyer

We consider a monopolist seller with n heterogeneous items, facing a single buyer. The buyer hasa value for each item drawn independently according to(non-identical) distributions, and his value for a set ofitems is additive. The seller aims to maximize his revenue.It is known that an optimal mechanism in this setting maybe quite complex, requiring randomization [19] and menusof infinite size [15]. Hart and Nisan [17] have initiated astudy of two very simple pricing schemes for this setting:item pricing, in which each item is priced at its monopolyreserve; and bundle pricing, in which the entire set ofitems is priced and sold as one bundle. Hart and Nisan [17]have shown that neither scheme can guarantee more thana vanishingly small fraction of the optimal revenue. Insharp contrast, we show that for any distributions, thebetter of item and bundle pricing is a constant-factorapproximation to the optimal revenue. We further discussextensions to multiple buyers and to valuations that arecorrelated across items.

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

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

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

[4]  Lawrence M. Ausubel,et al.  The Lovely but Lonely Vickrey Auction , 2004 .

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

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

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

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

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

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

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

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

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

[14]  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.

[15]  Noam Nisan,et al.  Approximate revenue maximization with multiple items , 2012, EC '12.

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

[17]  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.

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

[19]  S. Matthew Weinberg,et al.  Symmetries and optimal multi-dimensional mechanism design , 2012, EC '12.

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

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

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

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

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

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

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

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

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

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

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

[31]  S. Matthew Weinberg,et al.  A Simple and Approximately Optimal Mechanism for an Additive Buyer , 2014, FOCS.

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

[33]  Tim Roughgarden,et al.  Revenue maximization with a single sample , 2015, Games Econ. Behav..

[34]  Andrew Chi-Chih Yao,et al.  An n-to-1 Bidder Reduction for Multi-item Auctions and its Applications , 2014, SODA.

[35]  Mohammad Taghi Hajiaghayi,et al.  Revenue Maximization for Selling Multiple Correlated Items , 2014, ESA.

[36]  Michal Feldman,et al.  Combinatorial Auctions via Posted Prices , 2014, SODA.

[37]  Xi Chen,et al.  On the Complexity of Optimal Lottery Pricing and Randomized Mechanisms , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[38]  S. Matthew Weinberg,et al.  Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity , 2018, ACM Trans. Economics and Comput..

[39]  S. Hart,et al.  Maximal revenue with multiple goods: Nonmonotonicity and other observations , 2015 .

[40]  Nikhil R. Devanur,et al.  The sample complexity of auctions with side information , 2015, STOC.