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Optimal Efficiency Guarantees for Network Design Mechanisms

  • Tim Roughgarden
  • Mukund Sundararajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4513)

Abstract

A cost-sharing problem is defined by a set of players vying to receive some good or service, and a cost function describing the cost incurred by the auctioneer as a function of the set of winners. A cost-sharing mechanism is a protocol that decides which players win the auction and at what prices. Three desirable but provably mutually incompatible properties of a cost-sharing mechanism are: incentive-compatibility, meaning that players are motivated to bid their true private value for receiving the good; budget-balance, meaning that the mechanism recovers its incurred cost with the prices charged; and efficiency, meaning that the cost incurred and the value to the players served are traded off in an optimal way.

Our work is motivated by the following fundamental question: for which cost-sharing problems are incentive-compatible mechanisms with good approximate budget-balance and efficiency possible? We focus on cost functions defined implicitly by NP-hard combinatorial optimization problems, including the metric uncapacitated facility location problem, the Steiner tree problem, and rent-or-buy network design problems. For facility location and rent-or-buy network design, we establish for the first time that approximate budget-balance and efficiency are simultaneously possible. For the Steiner tree problem, where such a guarantee was previously known, we prove a new, optimal lower bound on the approximate efficiency achievable by the wide and natural class of “Moulin mechanisms”. This lower bound exposes a latent approximation hierarchy among different cost-sharing problems.

Keywords

Cost Function Network Design Facility Location Steiner Tree Budget Balance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Tim Roughgarden
    • 1
  • Mukund Sundararajan
    • 1
  1. 1.Department of Computer Science, Stanford University, 353 Serra Mall, Stanford, CA 94305 

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