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Computation of Nash Equilibria of Attack and Defense Games on Networks

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Algorithmic Game Theory (SAGT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14238))

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Abstract

We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the network. We propose an algorithm that runs in \(O(n^4)\) time with respect to the number of nodes of the network, n.

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Notes

  1. 1.

    Throughout the paper when using the term path we will mean a simple path.

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Acknowledgements

This work was supported by the Polish National Science Centre through grant 2018/29/B/ST6/00174.

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Authors and Affiliations

  1. University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Banacha 2, 02-097, Warsaw, Poland

    Stanisław Kaźmierowski & Marcin Dziubiński

Authors
  1. Stanisław Kaźmierowski
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  2. Marcin Dziubiński
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Correspondence to Stanisław Kaźmierowski .

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Editors and Affiliations

  1. Royal Holloway University of London, Egham, UK

    Argyrios Deligkas

  2. University of Edinburgh, Edinburgh, UK

    Aris Filos-Ratsikas

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Kaźmierowski, S., Dziubiński, M. (2023). Computation of Nash Equilibria of Attack and Defense Games on Networks. In: Deligkas, A., Filos-Ratsikas, A. (eds) Algorithmic Game Theory. SAGT 2023. Lecture Notes in Computer Science, vol 14238. Springer, Cham. https://doi.org/10.1007/978-3-031-43254-5_1

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  • DOI: https://doi.org/10.1007/978-3-031-43254-5_1

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  • Print ISBN: 978-3-031-43253-8

  • Online ISBN: 978-3-031-43254-5

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