3 papers
math.OC2019
Unique ergodicity of deterministic zero-sum differential games
Antoine Hochart
We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon di…
math.OC2018
A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors
Marianne Akian, Stéphane Gaubert, Antoine Hochart
We establish a generalized Perron-Frobenius theorem, based on a combinatorial criterion which entails the existence of an eigenvector for any nonlinear order-preserving and positiv…
math.OC2016
An Accretive Operator Approach to Ergodic Problems for Zero-Sum Games
Antoine Hochart
Mean payoff stochastic games can be studied by means of a nonlinear spectral problem involving the Shapley operator: the ergodic equation. A solution consists in a scalar, called t…