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Differential Games in $$L^{\infty }$$ L ∞

Author

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  • E. N. Barron

    (Loyola University Chicago)

Abstract

The Isaacs equations for differential games in $${L^{\infty }}$$ L ∞ first derived in Barron (Nonlinear Anal 14:971–989, 1990) are reformulated so that the Hamiltonians are continuous and result in a simpler problem to analyze numerically. Relaxed differential games in $${L^{\infty }}$$ L ∞ are considered. $$L^{\infty }$$ L ∞ differential games with time and state independent dynamics and convex or quasiconvex terminal data are solved explicitly using a type of Hopf–Lax formula. The stochastic differential game in $${L^{\infty }}$$ L ∞ connected to stochastic target problems is also discussed.

Suggested Citation

  • E. N. Barron, 2017. "Differential Games in $$L^{\infty }$$ L ∞," Dynamic Games and Applications, Springer, vol. 7(2), pages 157-184, June.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:2:d:10.1007_s13235-016-0183-5
    DOI: 10.1007/s13235-016-0183-5
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    References listed on IDEAS

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    1. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    2. repec:dau:papers:123456789/6046 is not listed on IDEAS
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