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  The Price of Anarchy on Uniformly Related Machines Revisited

Epstein, L., & van Stee, R. (2008). The Price of Anarchy on Uniformly Related Machines Revisited. In B. Monien, & U.-P. Schroeder (Eds.), Algorithmic Game Theory (pp. 46-57). Berlin: Springer. doi:10.1007/978-3-540-79309-0_6.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-1D32-6 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0028-F32F-3
Genre: Conference Paper

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 Creators:
Epstein, Leah1, Author
van Stee, Rob2, Author           
Affiliations:
1External Organizations, ou_persistent22              
2Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Recent interest in Nash equilibria led to a study of the {\it price of anarchy} (PoA) and the {\it strong price of anarchy} (SPoA) for scheduling problems. The two measures express the worst case ratio between the cost of an equilibrium (a pure Nash equilibrium, and a strong equilibrium, respectively) to the cost of a social optimum. We consider scheduling on uniformly related machines. Here the atomic players are the jobs, and the delay of a job is the completion time of the machine running it, also called the load of this machine. The social goal is to minimize the maximum delay of any job, while the selfish goal of each job is to minimize its own delay, that is, the delay of the machine running it. While previous studies either consider identical speed machines or an arbitrary number of speeds, focusing on the number of machines as a parameter, we consider the situation in which the number of different speeds is small. We reveal a linear dependence between the number of speeds and the poa. For a set of machines of at most $p$ speeds, the PoA turns out to be exactly $p+1$. The growth of the PoA for large numbers of related machines is therefore a direct result of the large number of potential speeds. We further consider a well known structure of processors, where all machines are of the same speed except for one possibly faster machine. We investigate the PoA as a function of both the speed of the fastest machine and the number of slow machines, and give tight bounds for nearly all cases.

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Language(s): eng - English
 Dates: 2009-03-0320082008
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 428068
DOI: 10.1007/978-3-540-79309-0_6
URI: http://www.springerlink.com/content/9883p3h807717292/fulltext.pdf
Other: Local-ID: C125756E0038A185-EA2DADF8C39471CEC125753C00401339-vanStee2008
 Degree: -

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Title: First International Symposium on
Place of Event: Paderborn, Germany
Start-/End Date: 2009-04-30 - 2009-05-02

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Title: Algorithmic Game Theory
  Subtitle : First International Symposium, SAGT 2008, Paderborn, Germany, April 30-May 2, 2008. Proceedings
  Abbreviation : SAGT 2008
Source Genre: Proceedings
 Creator(s):
Monien, Burkhard1, Editor
Schroeder, Ulf-Peter1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Berlin : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 46 - 57 Identifier: -

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Title: Lecture Notes in Computer Science
  Abbreviation : LNCS
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 4997 Sequence Number: - Start / End Page: - Identifier: ISSN: 0302-9743