Journal of Combinatorial Optimization

, Volume 37, Issue 2, pp 620–638 | Cite as

Pure Nash equilibria in restricted budget games

  • Maximilian DreesEmail author
  • Matthias Feldotto
  • Sören Riechers
  • Alexander Skopalik


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.


Congestion games Pure Nash equilibrium Existence Convergence Complexity Approximation 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Maximilian Drees
    • 1
    Email author
  • Matthias Feldotto
    • 2
  • Sören Riechers
    • 2
  • Alexander Skopalik
    • 2
  1. 1.University of TwenteEnschedeThe Netherlands
  2. 2.Paderborn UniversityPaderbornGermany

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