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- Guillaume Vigeral
- Dynamic Games and Applications
- 2013

We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does notâ€¦ (More)

In an optimal control framework, we consider the value VT (x) of the problem starting from state x with finite horizon T , as well as the value WÎ»(x) of the Î»-discounted problem starting from x. Weâ€¦ (More)

We consider an operator Î¨ defined on a set of real valued functions and satisfying two properties of monotonicity and additive homogeneity. This is motivated by the case of zero sum stochastic games,â€¦ (More)

- Sylvain Sorin, Guillaume Vigeral
- J. Optimization Theory and Applications
- 2013

We give new proofs of existence of the limit of the discounted values for two person zero-sum games in the following frameworks: incomplete information, absorbing, recursive. The idea of these newâ€¦ (More)

- JÃ©rÃ´me Bolte, StÃ©phane Gaubert, Guillaume Vigeral
- Math. Oper. Res.
- 2015

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such gamesâ€¦ (More)

We establish a maximin characterisation of the linear escape rate of the orbits of a non-expansive mapping on a complete (hemi-)metric space, under a mild form of Busemannâ€™s non-positive curvatureâ€¦ (More)

We consider some discrete and continuous dynamics in a Banach space involving a non expansive operator J and a corresponding family of strictly contracting operators Î¦(Î», x) := Î»J( 1âˆ’Î» Î» x) for Î» âˆˆâ€¦ (More)

- Sylvain Sorin, Guillaume Vigeral
- Int. J. Game Theory
- 2016

We study the links between the values of stochastic games with varying stage duration h, the corresponding Shapley operators T and Th = hT+ (1âˆ’ h)Id and the solution of the evolution equation á¸Ÿt = (Tâ€¦ (More)

We show in a dynamic programming framework that uniform convergence of the finite horizon values implies that asymptotically the average accumulated payoff is constant on optimal trajectories. Weâ€¦ (More)

We consider some discrete and continuous dynamics in a Banach space involving a non expansive operator J and a corresponding family of strictly contracting operators Î¦(Î», x) := Î»J( 1âˆ’Î» Î» x) for Î»â€¦ (More)