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LP-Based Covering Games with Low Price of Anarchy

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Abstract

We design a new class of vertex and set cover games, where 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. This is in contrast to all previously studied covering games, where the price of anarchy grows linearly with the size of the game. Both the game design and the price of anarchy results are based on structural properties of the linear programming relaxations. For linear costs we also exhibit simple best response dynamics that converge to Nash equilibria in linear time.

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Notes

  1. These are the dynamics where each agent takes turn playing his best response in a cyclic ordering according to some fixed permutation.

  2. In our games, the set of strategies is infinite as ransoms can be arbitrary real numbers. However, if the vertex weights are integers, we can restrict possible ransoms to be integers as well. All results of the paper straightforwardly extend to this finite game.

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Acknowledgements

Georgios Piliouras was supported by AFOSR project FA9550-09-1-0538, while working at the School of Electrical & Computer Engineering, Georgia Institute of Technology. Tomáš Valla was supported by the Centre of Excellence – Institute for Theoretical Computer Science (project P202/12/G061 of GA ČR), and by the GAUK Project 66010. László A. Végh was supported by NSF Grant CCF-0914732, while working at the College of Computing, Georgia Institute of Technology,

We would like to thank Jarik Nešetřil for inspiring us to work on this problem and for a generous support in all directions.

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Authors and Affiliations

  1. Computing & Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA

    Georgios Piliouras

  2. Faculty of Information Technology, Czech Technical University, Prague, Czech Republic

    Tomáš Valla

  3. Department of Management, London School of Economics, London, UK

    László A Végh

Authors
  1. Georgios Piliouras
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  2. Tomáš Valla
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  3. László A Végh
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Correspondence to Tomáš Valla.

Additional information

This work was done while the first and third authors were working at the Georgia Institute of Technology, Atlanta, GA.

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Piliouras, G., Valla, T. & Végh, L.A. LP-Based Covering Games with Low Price of Anarchy. Theory Comput Syst 57, 238–260 (2015). https://doi.org/10.1007/s00224-014-9587-z

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