Random Zero-Sum Dynamic Games on Infinite Directed Graphs

Luc Attia (), Lyuben Lichev (), Dieter Mitsche (), Raimundo Saona () and Bruno Ziliotto ()
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Luc Attia: Paris Dauphine University
Lyuben Lichev: University Jean Monnet
Dieter Mitsche: University Jean Monnet
Raimundo Saona: Institute of Science and Technology Austria
Bruno Ziliotto: CNRS UMR 5219

Dynamic Games and Applications, 2025, vol. 15, issue 5, No 1, 1517-1535

Abstract: 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.

Keywords: Zero-sum games; Dynamic games; Random games; Directed graphs; 91A05; 91A10; 91A25; 91A50; 05C05; 05C63 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13235-025-00636-4

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