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A Simple Mechanism for a Budget-Constrained Buyer

  • Yu Cheng
  • Nick Gravin
  • Kamesh Munagala
  • Kangning WangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11316)

Abstract

We study a classic Bayesian mechanism design setting of monopoly problem for an additive buyer in the presence of budgets. In this setting a monopolist seller with m heterogeneous items faces a single buyer and seeks to maximize her revenue. The buyer has a budget and additive valuations drawn independently for each item from (non-identical) distributions. We show that when the buyer’s budget is publicly known, the better of selling each item separately and selling the grand bundle extracts a constant fraction of the optimal revenue. When the budget is private, we consider a standard Bayesian setting where buyer’s budget b is drawn from a known distribution B. We show that if b is independent of the valuations and distribution B satisfies monotone hazard rate condition, then selling items separately or in a grand bundle is still approximately optimal. We give a complementary example showing that no constant approximation simple mechanism is possible if budget b can be interdependent with valuations.

Notes

Acknowledgements

Yu Cheng is supported by NSF grants CCF-1527084, CCF-1535972, CCF-1637397, CCF-1704656, IIS-1447554, and NSF CAREER Award CCF-1750140. Kamesh Munagala is supported by NSF grants CCF-1408784, CCF-1637397, and IIS-1447554; and by an Adobe Data Science Research Award. Kangning Wang is supported by NSF grants CCF-1408784 and CCF-1637397.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Yu Cheng
    • 1
  • Nick Gravin
    • 2
  • Kamesh Munagala
    • 1
  • Kangning Wang
    • 1
    Email author
  1. 1.Duke UniversityDurhamUSA
  2. 2.Shanghai University of Finance and EconomicsShanghaiChina

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