Value in mixed strategies for zero-sum stochastic differential games without Isaacs condition - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Annals of Probability Année : 2014

Value in mixed strategies for zero-sum stochastic differential games without Isaacs condition

Résumé

In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the problem of the existence of a value without Isaacs condition. Not surprising, this requires a suitable concept of mixed strategies which, to the authors' best knowledge, was not known in the context of stochastic differential games. For this, we consider nonanticipative strategies with a delay defined through a partition $\pi$ of the time interval $[0,T]$. The underlying stochastic controls for the both players are randomized along $\pi$ by a hazard which is independent of the governing Brownian motion, and knowing the information available at the left time point $t_{j-1}$ of the subintervals generated by $\pi$, the controls of Players 1 and 2 are conditionally independent over $[t_{j-1},t_j)$. It is shown that the associated lower and upper value functions $W^{\pi}$ and $U^{\pi}$ converge uniformly on compacts to a function $V$, the so-called value in mixed strategies, as the mesh of $\pi$ tends to zero. This function $V$ is characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs equation.
Fichier principal
Vignette du fichier
1407.7326v1.pdf (415.24 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01098230 , version 1 (05-01-2015)

Identifiants

Citer

Rainer Buckdahn, Juan Li, Marc Quincampoix. Value in mixed strategies for zero-sum stochastic differential games without Isaacs condition. Annals of Probability, 2014, 42 (4), pp.1724 - 1768. ⟨10.1214/13-AOP849⟩. ⟨hal-01098230⟩
261 Consultations
96 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More