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Value Function of Differential Games without Isaacs Conditions. An Approach with Non-Anticipative Mixed Strategies

Abstract : In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are associated with classical nonanticipative strategies (with delay). Imposing on the underlying controls for both players a conditional independence property, we obtain the existence of the value in mixed strategies as the limit of the lower as well as of the upper value functions along a sequence of partitions which mesh tends to zero. Moreover, we characterize this value in mixed strategies as the unique viscosity solution of the corresponding Hamilton-Jacobi-Isaacs equation.
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https://hal.inria.fr/hal-00800185
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, March 13, 2013 - 12:27:43 PM
Last modification on : Wednesday, April 1, 2020 - 1:57:03 AM

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Rainer Buckdahn, Juan Li, Marc Quincampoix. Value Function of Differential Games without Isaacs Conditions. An Approach with Non-Anticipative Mixed Strategies. International Journal of Game Theory, Springer Verlag, 2013, 42 (4), pp.989-1020. ⟨10.1007/s00182-012-0351-9⟩. ⟨hal-00800185⟩

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