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Algorithms as mechanisms: the price of anarchy of relax-and-round

Algorithms as mechanisms: the price of anarchy of relax-and-round Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round ¨ PAUL DUTTING, ETH Z¨rich u and THOMAS KESSELHEIM, Max-Planck-Institut f¨r Informatik u and ´ EVA TARDOS, Cornell University We show that algorithms that follow the relax-and-round paradigm translate approximation guarantees into Price of Anarchy guarantees, provided that the rounding is oblivious and the relaxation is smooth. We use this meta result to obtain simple, near-optimal mechanisms for a broad range of optimization problems such as combinatorial auctions, the maximum traveling salesman problem, and packing integer programs. In each case the resulting mechanism matches or beats the performance guarantees of known mechanisms. Categories and Subject Descriptors: F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; J.4 [Computer Applications]: Social and Behavioral Sciences-- Economics General Terms: Algorithms, Economics, Theory Additional Key Words and Phrases: Algorithmic Game Theory, Price of Anarchy, Smoothness, Black-Box Reductions 1. INTRODUCTION The "classic" approach to mechanism design is to devise mechanisms that incentivize truthful reporting. For settings where the private information of each agent consists of a single number this boils down to finding allocation rules that are monotone in each agent's private value. Many natural approximation algorithms either satisfy this monotonicity constraint or can http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Algorithms as mechanisms: the price of anarchy of relax-and-round

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Association for Computing Machinery
Copyright
Copyright © 2016 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/2904104.2904107
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Abstract

Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round ¨ PAUL DUTTING, ETH Z¨rich u and THOMAS KESSELHEIM, Max-Planck-Institut f¨r Informatik u and ´ EVA TARDOS, Cornell University We show that algorithms that follow the relax-and-round paradigm translate approximation guarantees into Price of Anarchy guarantees, provided that the rounding is oblivious and the relaxation is smooth. We use this meta result to obtain simple, near-optimal mechanisms for a broad range of optimization problems such as combinatorial auctions, the maximum traveling salesman problem, and packing integer programs. In each case the resulting mechanism matches or beats the performance guarantees of known mechanisms. Categories and Subject Descriptors: F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; J.4 [Computer Applications]: Social and Behavioral Sciences-- Economics General Terms: Algorithms, Economics, Theory Additional Key Words and Phrases: Algorithmic Game Theory, Price of Anarchy, Smoothness, Black-Box Reductions 1. INTRODUCTION The "classic" approach to mechanism design is to devise mechanisms that incentivize truthful reporting. For settings where the private information of each agent consists of a single number this boils down to finding allocation rules that are monotone in each agent's private value. Many natural approximation algorithms either satisfy this monotonicity constraint or can

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ACM SIGecom Exchanges – Association for Computing Machinery

Published: Mar 16, 2016

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