Pure and Random strategies in differential game with incomplete informations
Cardaliaguet, Pierre; Jimenez, Chloé; Quincampoix, Marc (2014), Pure and Random strategies in differential game with incomplete informations, Journal of Dynamics and Games, 1, 3, p. 363 - 375. http://dx.doi.org/10.3934/jdg.2014.1.363
TypeArticle accepté pour publication ou publié
Journal nameJournal of Dynamics and Games
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Abstract (EN)We investigate a two players zero sum differential game with incomplete information on the initial state: The first player has a private information on the initial state while the second player knows only a probability distribution on the initial state. This could be view as a generalization to differential games of the famous Aumann-Maschler framework for repeated games. In an article of the first author, the existence of the value in random strategies was obtained for a finite number of initial conditions (the probability distribution is a finite combination of Dirac measures). The main novelty of the present work consists in : first extending the result on the existence of a value in random strategies for infinite number of initial conditions and second - and mainly - proving the existence of a value in pure strategies when the initial probability distribution is regular enough (without atoms).
Subjects / KeywordsWasserstein distance; purification; incomplete information; zero-sum games; Differential games
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