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Random Zero-Sum Dynamic Games on Infinite Directed Graphs

Author

Listed:
  • Luc Attia

    (Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres, CNRS - Centre National de la Recherche Scientifique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Lyuben Lichev

    (IST Austria - Institute of Science and Technology [Klosterneuburg, Austria])

  • Dieter Mitsche

    (UC - Pontificia Universidad Católica de Chile)

  • Raimundo Saona

    (IST Austria - Institute of Science and Technology [Klosterneuburg, Austria])

  • Bruno Ziliotto

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider random two-player zero-sum dynamic games with perfect information on a class of infinite directed graphs. Starting from a fixed vertex, the players take turns to move a token along the edges of the graph. Every vertex is assigned a payoff known in advance by both players. Every time the token visits a vertex, Player 2 pays Player 1 the corresponding payoff. We consider a distribution over such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that, when the duration of the game tends to infinity, the value converges almost surely to a constant at an exponential rate dominated in terms of the expansion. On 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.

Suggested Citation

  • Luc Attia & Lyuben Lichev & Dieter Mitsche & Raimundo Saona & Bruno Ziliotto, 2025. "Random Zero-Sum Dynamic Games on Infinite Directed Graphs," Post-Print hal-05092326, HAL.
    • Handle: RePEc:hal:journl:hal-05092326
    DOI: 10.1007/s13235-025-00636-4
    as

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