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Pure and Random strategies in differential game with incomplete informations

Abstract : 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).
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https://hal.inria.fr/hal-01068412
Contributor : Estelle Bouzat <>
Submitted on : Thursday, September 25, 2014 - 4:02:06 PM
Last modification on : Monday, October 5, 2020 - 11:30:03 AM

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Pierre Cardaliaguet, Chloé Jimenez, Marc Quincampoix. Pure and Random strategies in differential game with incomplete informations. Journal of Dynamics and Games, AIMS, 2014, 1 (3), pp.363 - 375. ⟨10.3934/jdg.2014.1.363⟩. ⟨hal-01068412⟩

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