Zero-sum Random Games on Directed Graphs
Optimization and Control
2024-01-30 v1
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 -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.
Cite
@article{arxiv.2401.16252,
title = {Zero-sum Random Games on Directed Graphs},
author = {Luc Attia and Lyuben Lichev and Dieter Mitsche and Raimundo Saona and Bruno Ziliotto},
journal= {arXiv preprint arXiv:2401.16252},
year = {2024}
}