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Covering Games: Approximation through Non-cooperation

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Internet and Network Economics (WINE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5929))

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Abstract

We propose approximation algorithms under game-theoretic considerations. We indroduce and study the general covering problem which is a natural generalization of the well-studied max-n -cover problem. In the general covering problem, we are given a universal set of weighted elements E and n collections of subsets of the elements. The task is to choose one subset from each collection such that the total weight of their union is as large as possible. In our game-theoretic setting, the choice in each collection is made by an independent player. For covering an element, the players receive a payoff defined by a non-increasing utility sharing function. This function defines the fraction that each covering player receives from the weight of the elements. We show how to construct a utility sharing function such that every Nash Equilibrium approximates the optimal solution by a factor of \(1-{{1} \over {e}}\). We also prove that any sequence of unilateral improving steps is polynomially bounded. This gives rise to a polynomial-time local search approximation algorithm whose approximation ratio is best possible.

This work was supported by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD).

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Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, U.K.

    Martin Gairing

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  1. Martin Gairing
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Editors and Affiliations

  1. Department of Information and Systems, Sapienza University of Rome, Via Ariosto 25, 00185, Roma, Italy

    Stefano Leonardi

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Gairing, M. (2009). Covering Games: Approximation through Non-cooperation. In: Leonardi, S. (eds) Internet and Network Economics. WINE 2009. Lecture Notes in Computer Science, vol 5929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10841-9_18

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  • DOI: https://doi.org/10.1007/978-3-642-10841-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10840-2

  • Online ISBN: 978-3-642-10841-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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