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LP-based Covering Games with Low Price of Anarchy

Piliouras, Georgios, Valla, Tomas and Végh, László A. ORCID: 0000-0003-1152-200X (2012) LP-based Covering Games with Low Price of Anarchy. In: WINE 2012 - Workshop on Internet & Network Economics, 2012-12-01, Liverpool, United Kingdom, GBR.

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We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3].

Item Type: Conference or Workshop Item (Paper)
Additional Information: © 2012 The Author
Divisions: Mathematics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited: 03 Dec 2014 09:53
Last Modified: 16 May 2024 11:07

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