Value function of differential games without Isaacs conditions. An approach with nonanticipative mixed strategies

Rainer Buckdahn (), Juan Li () and Marc Quincampoix ()

International Journal of Game Theory, 2013, vol. 42, issue 4, 989-1020

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. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: 2-person zero-sum differential games; Isaacs condition; Dynamic programming principle; Nonanticipative strategy with delay; Viscosity solution; Value function (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:42:y:2013:i:4:p:989-1020

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DOI: 10.1007/s00182-012-0351-9

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