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Pure Nash Equilibria in Restricted Budget Games

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Computing and Combinatorics (COCOON 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10392))

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Abstract

In budget games, players compete over resources with finite budgets. For every resource, a player has a specific demand and as a strategy, he chooses a subset of resources. If the total demand on a resource does not exceed its budget, the utility of each player who chose that resource equals his demand. Otherwise, the budget is shared proportionally. In the general case, pure Nash equilibria (NE) do not exist for such games. In this paper, we consider the natural classes of singleton and matroid budget games with additional constraints and show that for each, pure NE can be guaranteed. In addition, we introduce a lexicographical potential function to prove that every matroid budget game has an approximate pure NE which depends on the largest ratio between the different demands of each individual player.

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901).

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Authors and Affiliations

  1. Departement of Applied Mathematics, University of Twente, Enschede, The Netherlands

    Maximilian Drees

  2. Department of Computer Science and Heinz Nixdorf Institute, Paderborn University, Paderborn, Germany

    Matthias Feldotto, Sören Riechers & Alexander Skopalik

Authors
  1. Maximilian Drees
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  2. Matthias Feldotto
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  3. Sören Riechers
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  4. Alexander Skopalik
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Correspondence to Maximilian Drees .

Editor information

Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Yixin Cao

  2. Texas A&M University, College Station, Texas, USA

    Jianer Chen

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Drees, M., Feldotto, M., Riechers, S., Skopalik, A. (2017). Pure Nash Equilibria in Restricted Budget Games. In: Cao, Y., Chen, J. (eds) Computing and Combinatorics. COCOON 2017. Lecture Notes in Computer Science(), vol 10392. Springer, Cham. https://doi.org/10.1007/978-3-319-62389-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-62389-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62388-7

  • Online ISBN: 978-3-319-62389-4

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