7 citations · 10 across the 5 of their papers we have counts for
10 papers
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…
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…
An accretive operator approach to ergodic zero-sum stochastic games
Antoine Hochart
We study some ergodicity property of zero-sum stochastic games with a finite state space and possibly unbounded payoffs. We formulate this property in operator-theoretical terms, i…
Qualification Conditions in Semi-algebraic Programming
Jérôme Bolte, Antoine Hochart, Edouard Pauwels
For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding inequality constraint set and we study qualification conditions for perturbation…
Generic uniqueness of the bias vector of finite stochastic games with perfect information
Marianne Akian, Stéphane Gaubert, Antoine Hochart
Mean-payoff zero-sum stochastic games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair s…
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…
Minimax representation of nonexpansive functions and application to zero-sum recursive games
Marianne Akian, Stéphane Gaubert, Antoine Hochart
We show that a real-valued function on a topological vector space is positively homogeneous of degree one and nonexpansive with respect to a weak Minkowski norm if and only if it c…
Hypergraph conditions for the solvability of the ergodic equation for zero-sum games
Marianne Akian, Stéphane Gaubert, Antoine Hochart
The ergodic equation is a basic tool in the study of mean-payoff stochastic games. Its solvability entails that the mean payoff is independent of the initial state. Moreover, optim…
Generic uniqueness of the bias vector of mean payoff zero-sum games
Marianne Akian, Stéphane Gaubert, Antoine Hochart
Zero-sum mean payoff games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair solution of…
Ergodicity conditions for zero-sum games
Marianne Akian, Stéphane Gaubert, Antoine Hochart
A basic question for zero-sum repeated games consists in determining whether the mean payoff per time unit is independent of the initial state. In the special case of "zero-player"…