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Pure Nash Equilibria in a Generalization of Congestion Games Allowing Resource Failures

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Algorithmic Game Theory (SAGT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12885))

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Abstract

We introduce a model for congestion games in which resources can fail with some probability distribution. These games are an extension of classical congestion games, and like these, have exact potential functions that guarantee the existence of pure Nash equilibria (PNE). We prove that the agent’s cost functions for these games can be hard to compute by giving an example of a game for which the cost function is hard for Valiant’s class, even in the case when all failure probabilities coincide. We characterize the complexity of computing PNE in congestion games with failures with an extension of the local search class PLS that allows queries to a function, and show examples of games for which the PNE search problem is complete for this class. We also provide a variant of the game with the property that a PNE can be constructed in polynomial time if this also holds in the restricted game without failures.

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Authors and Affiliations

  1. Institute of Theoretical Computer Science, Ulm University, Ulm, Germany

    Julian Nickerl & Jacobo Torán

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  1. Julian Nickerl
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  2. Jacobo Torán
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Correspondence to Julian Nickerl .

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Editors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Ioannis Caragiannis

  2. Aarhus University, Aarhus, Denmark

    Kristoffer Arnsfelt Hansen

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Nickerl, J., Torán, J. (2021). Pure Nash Equilibria in a Generalization of Congestion Games Allowing Resource Failures. In: Caragiannis, I., Hansen, K.A. (eds) Algorithmic Game Theory. SAGT 2021. Lecture Notes in Computer Science(), vol 12885. Springer, Cham. https://doi.org/10.1007/978-3-030-85947-3_13

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  • DOI: https://doi.org/10.1007/978-3-030-85947-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85946-6

  • Online ISBN: 978-3-030-85947-3

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