Pure Nash equilibria in restricted budget games

Maximilian Drees, Matthias Feldotto, Sören Riechers, Alexander Skopalik

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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.
Original languageEnglish
Pages (from-to)620-638
Number of pages19
JournalJournal of combinatorial optimization
Issue number2
Early online date17 Mar 2018
Publication statusPublished - 15 Feb 2019


  • Congestion games
  • Pure Nash equilibrium
  • Existence
  • Convergence
  • Complexity
  • Approximation


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