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arXiv · 2401.16252

Zero-sum Random Games on Directed Graphs

Luc Attia·Lyuben Lichev·Dieter Mitsche·Raimundo Saona·Bruno Ziliotto
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Abstract

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. Starting from a fixed vertex, players take turns to move a token along the edges of the graph. On 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. 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 in terms of the expansion.

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Luc Attia, Lyuben Lichev, Dieter Mitsche, Raimundo Saona, Bruno Ziliotto. 2024-01-29. Zero-sum Random Games on Directed Graphs. https://arxiv.org/abs/2401.16252

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