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A common generalization of budget games and congestion games

Author

Listed:
  • Fuga Kiyosue

    (SCSK Corporation)

  • Kenjiro Takazawa

    (Hosei University)

Abstract

Budget games were introduced by Drees, Riechers, and Skopalik (2014) as a model of noncooperative games arising from resource allocation problems. Budget games have several similarities to congestion games, one of which is that the matroid structure of the strategy space is essential for the existence of a pure Nash equilibrium (PNE). Despite these similarities, however, the theoretical relation between budget games and congestion games has been unclear. In this paper, we provide a common generalization of budget games and congestion games, called generalized budget games (g-budget games, for short), to establish a large class of noncooperative games retaining the nice property of the matroid structure. We show that the model of g-budget games includes weighted congestion games and player-specific congestion games under certain assumptions. We further show that g-budget games also include offset budget games, a generalized model of budget games by Drees, Feldotto, Riechers, and Skopalik (2019). We then prove that every matroid g-budget game has a PNE, which extends the result for budget games. We finally a PNE in a certain class of singleton g-budget games can be computed in a greedy manner.

Suggested Citation

  • Fuga Kiyosue & Kenjiro Takazawa, 2024. "A common generalization of budget games and congestion games," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-18, October.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:3:d:10.1007_s10878-024-01218-7
    DOI: 10.1007/s10878-024-01218-7
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    References listed on IDEAS

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    1. Satoru Fujishige & Michel X. Goemans & Tobias Harks & Britta Peis & Rico Zenklusen, 2017. "Matroids Are Immune to Braess’ Paradox," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 745-761, August.
    2. Kenjiro Takazawa, 2019. "Generalizations of weighted matroid congestion games: pure Nash equilibrium, sensitivity analysis, and discrete convex function," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1043-1065, November.
    3. Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 461-482, May.
    4. repec:cup:cbooks:9781316779309 is not listed on IDEAS
    5. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781316624791.
    6. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781107172661.
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