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A zero sum differential game with correlated informations on the initial position. A case with a continuum of initial positions

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  • We study a two player zero sum game where the initial position $ z_0 $ is not communicated to any player. The initial position is a function of a couple $ (x_0,y_0) $ where $ x_0 $ is communicated to player Ⅰ while $ y_0 $ is communicated to player Ⅱ. The couple $ (x_0,y_0) $ is chosen according to a probability measure $ dm(x,y) = h(x,y) d\mu(x) d\nu(y) $. We show that the game has a value and, under additional regularity assumptions, that the value is a solution of Hamilton Jacobi Isaacs equation in a dual sense.

    Mathematics Subject Classification: 49N70, 49L25, 91A23, 49Q20.


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