Pure and Random strategies in differential game with incomplete informations

Pierre Cardaliaguet; Chloé Jimenez; Marc Quincampoix

doi:10.3934/jdg.2014.1.363

Article Contents

2014, Volume 1, Issue 3: 363-375. Doi: 10.3934/jdg.2014.1.363

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Pure and Random strategies in differential game with incomplete informations

1.
CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75016 Paris
2.
Laboratoire de Mathématiques de Bretagne Atlantique, CNRS-UMR 6205, Université de Brest, 6, avenue Victor Le Gorgeu, CS 93837, 29238 Brest cedex 3

Received: October 31, 2012

Revised: April 30, 2013

Published: June 2014

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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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Mathematics Subject Classification: Primary: 49N70; Secondary: 91A05.

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References

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