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An Improved Bound for the Tree Conjecture in Network Creation Games

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Algorithmic Game Theory (SAGT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13584))

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Abstract

We study Nash equilibria in the network creation game of Fabrikant et al. [11]. In this game a vertex can buy an edge to another vertex for a cost of \(\alpha \), and the objective of each vertex is to minimize the sum of the costs of the edges it purchases plus the sum of the distances to every other vertex in the resultant network. A long-standing conjecture states that if \(\alpha \ge n\) then every Nash equilibrium in the game is a spanning tree. We prove the conjecture holds for any \(\alpha >3n-3\).

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Notes

  1. 1.

    A biconnected component \(H\subseteq G\) is a maximal set such that there are two vertex-disjoint paths between any pair of vertices in H.

  2. 2.

    The girth is infinite if G is a forest.

References

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Acknowledgements

We are grateful to the reviewers for comments and suggestions that helped improve this paper.

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Authors and Affiliations

  1. McGill University, Montreal, QC, H3A 0G4, Canada

    Jack Dippel & Adrian Vetta

Authors
  1. Jack Dippel
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  2. Adrian Vetta
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Correspondence to Jack Dippel .

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Editors and Affiliations

  1. University of Essex, Colchester, UK

    Panagiotis Kanellopoulos

  2. University of Essex, Colchester, UK

    Maria Kyropoulou

  3. University of Essex, Colchester, UK

    Alexandros Voudouris

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Dippel, J., Vetta, A. (2022). An Improved Bound for the Tree Conjecture in Network Creation Games. In: Kanellopoulos, P., Kyropoulou, M., Voudouris, A. (eds) Algorithmic Game Theory. SAGT 2022. Lecture Notes in Computer Science, vol 13584. Springer, Cham. https://doi.org/10.1007/978-3-031-15714-1_14

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  • DOI: https://doi.org/10.1007/978-3-031-15714-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15713-4

  • Online ISBN: 978-3-031-15714-1

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