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Pure Nash equilibria in restricted budget games

Author

Listed:
  • Maximilian Drees

    (University of Twente)

  • Matthias Feldotto

    (Paderborn University)

  • Sören Riechers

    (Paderborn University)

  • Alexander Skopalik

    (Paderborn University)

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.

Suggested Citation

  • Maximilian Drees & Matthias Feldotto & Sören Riechers & Alexander Skopalik, 2019. "Pure Nash equilibria in restricted budget games," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 620-638, February.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:2:d:10.1007_s10878-018-0269-7
    DOI: 10.1007/s10878-018-0269-7
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    References listed on IDEAS

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    1. Ioannis Caragiannis & Angelo Fanelli & Nick Gravin & Alexander Skopalik, 2015. "Approximate Pure Nash Equilibria in Weighted Congestion Games," Post-Print halshs-02094622, HAL.
    2. Chien, Steve & Sinclair, Alistair, 2011. "Convergence to approximate Nash equilibria in congestion games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 315-327, March.
    3. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
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