The communication requirements of efficient allocations and supporting prices

Noam Nisan, Ilya Segal*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

169 Scopus citations

Abstract

We show that any communication finding a value-maximizing allocation in a private-information economy must also discover supporting prices (in general personalized and nonlinear). In particular, to allocate L indivisible items between two agents, a price must be revealed for each of the 2L - 1 bundles. We prove that all monotonic prices for an agent must be used, hence exponential communication in L is needed. Furthermore, exponential communication is needed just to ensure a higher share of surplus than that realized by auctioning all items as a bundle, or even a higher expected surplus (for some probability distribution over valuations). When the utilities are submodular, efficiency still requires exponential communication (and fully polynomial approximation is impossible). When the items are identical, arbitrarily good approximation is obtained with exponentially less communication than exact efficiency.

Original languageAmerican English
Pages (from-to)192-224
Number of pages33
JournalJournal of Economic Theory
Volume129
Issue number1
DOIs
StatePublished - Jul 2006

Bibliographical note

Funding Information:
We are grateful to Paul Milgrom, Luis Rayo,Azeem Shaikh,Yoav Shoham, Steve Tadelis, Moshe Tenneholtz, and participants of seminars at Harvard-MIT, Princeton, Stanford, Toronto, and the 2002 DIMACS Workshop on Computational Issues in Game Theory and Mechanism Design for useful comments. N.N. was supported by a grant from the Israeli Academy of Sciences. I.S. was supported by the Guggenheim Foundation and the National Science Foundation (Grant SES-0214500), and was hosted by the Institute for Advanced Study in Princeton during his work on the project. Research assistance by Ronald Fadel and Hui Li is gratefully acknowledged.

Keywords

  • Approximation
  • Combinatorial auctions
  • Communication complexity
  • Distributional complexity
  • Homogenous items
  • Informational efficiency of prices
  • Message space dimension
  • Preference elicitation
  • Submodular valuations
  • Substitutable items

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