A differential game with a blind player

Pierre Cardaliaguet (1) , Anne Souquière (2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LM - Laboratoire de mathématiques de Brest
3 LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information

We consider a zero sum differential game with lack of observation on one side. The initial state of the system is drawn at random according to some probability $\mu_0$ on $\R^N$. Player I is informed of the initial position of state while player II knows only $\mu_0$. Moreover Player~I observes Player~II's moves while Player~II is blind and has no further information. We prove that in this game with a terminal payoff the value exists and is characterized as the unique viscosity solution of some Hamilton-Jacobi equation on a space of probability measures.

Mots clés: Differential games; Asymmetric information; Hamilton-Jacobi equations; Viscosity solutions; Wasserstein space.; Wasserstein space

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet, Anne Souquière. A differential game with a blind player. SIAM Journal on Control and Optimization, 2012, 50 (4), pp.2090--2116. ⟨hal-00520017⟩