arXiv subjects

Luc Attia

Publications and source records attributed to Luc Attia.

3 recordsLinked to original sources

arXiv2024

Zero-sum Random Games on Directed Graphs

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.

math.OC↗

arXiv2019

A formula for the value of a stochastic game

In 1953, Lloyd Shapley defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that competitive stochastic games have a discounted value. In 1982, Jean-François Mertens and Abraham Neyman proved that competitive stochastic games admit a robust solution concept, the value, which is equal to the limit of the discounted values as the discount rate goes to 0. Both contributions were published in PNAS. In the present paper, we provide a tractable formula for the value of competitive stochastic games.

math.PR↗

arXiv2019

Shapley-Snow kernels, multiparameter eigenvalue problems and stochastic games

We establish, for the first time, a connection between stochastic games and multiparameter eigenvalue problems, using the theory developed by Shapley and Snow (1950). This connection provides new results, new proofs, and new tools for studying stochastic games.

math.OC↗