---
_id: '17101'
abstract:
- lang: eng
  text: "This paper considers a class of two-player zero-sum games on directed graphs
    whose vertices are equipped with random payoffs of bounded support known by both
    players.\r\nStarting from a fixed vertex, players take turns to move a token along
    the edges of the graph.\r\nOn the one hand, for acyclic directed graphs of bounded
    degree and sub-exponential expansion, we show that the value of the game converges
    almost surely to a constant at an exponential rate dominated in terms of the expansion.\r\nOn
    the other hand, for the infinite d-ary tree that does not fall into the previous
    class of graphs, we show convergence at a double-exponential rate in terms of
    the expansion."
acknowledgement: "This work was supported by the French Agence Nationale de la Recherche
  (ANR) under references ANR-21-CE40-0020 (CONVERGENCE project) and ANR-20-CE40-0002
  (GrHyDy), and by Fondecyt grant 1220174. This collaboration was mainly conducted
  during a 1-year visit of Bruno Ziliotto to the Center for Mathematical Modeling
  (CMM) at University of Chile in 2023,\r\nunder the IRL program of CNRS."
article_number: '2401.16252'
article_processing_charge: No
arxiv: 1
author:
- first_name: Luc
  full_name: Attia, Luc
  last_name: Attia
- first_name: Lyuben
  full_name: Lichev, Lyuben
  last_name: Lichev
- first_name: Dieter
  full_name: Mitsche, Dieter
  last_name: Mitsche
- first_name: Raimundo J
  full_name: Saona Urmeneta, Raimundo J
  id: BD1DF4C4-D767-11E9-B658-BC13E6697425
  last_name: Saona Urmeneta
  orcid: 0000-0001-5103-038X
- first_name: Bruno
  full_name: Ziliotto, Bruno
  last_name: Ziliotto
citation:
  ama: Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Zero-sum random
    games on directed graphs. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2401.16252">10.48550/arXiv.2401.16252</a>
  apa: Attia, L., Lichev, L., Mitsche, D., Saona Urmeneta, R. J., &#38; Ziliotto,
    B. (n.d.). Zero-sum random games on directed graphs. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2401.16252">https://doi.org/10.48550/arXiv.2401.16252</a>
  chicago: Attia, Luc, Lyuben Lichev, Dieter Mitsche, Raimundo J Saona Urmeneta, and
    Bruno Ziliotto. “Zero-Sum Random Games on Directed Graphs.” <i>ArXiv</i>, n.d.
    <a href="https://doi.org/10.48550/arXiv.2401.16252">https://doi.org/10.48550/arXiv.2401.16252</a>.
  ieee: L. Attia, L. Lichev, D. Mitsche, R. J. Saona Urmeneta, and B. Ziliotto, “Zero-sum
    random games on directed graphs,” <i>arXiv</i>. .
  ista: Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Zero-sum random
    games on directed graphs. arXiv, 2401.16252.
  mla: Attia, Luc, et al. “Zero-Sum Random Games on Directed Graphs.” <i>ArXiv</i>,
    2401.16252, doi:<a href="https://doi.org/10.48550/arXiv.2401.16252">10.48550/arXiv.2401.16252</a>.
  short: L. Attia, L. Lichev, D. Mitsche, R.J. Saona Urmeneta, B. Ziliotto, ArXiv
    (n.d.).
date_created: 2024-06-03T07:45:22Z
date_published: 2024-01-29T00:00:00Z
date_updated: 2024-06-03T07:50:29Z
day: '29'
department:
- _id: KrCh
doi: 10.48550/arXiv.2401.16252
external_id:
  arxiv:
  - '2401.16252'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2401.16252
month: '01'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Zero-sum random games on directed graphs
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...