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

E. N. Barron ()
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E. N. Barron: Loyola University Chicago

Dynamic Games and Applications, 2017, vol. 7, issue 2, No 2, 157-184

Abstract: 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.

Keywords: Differential game; Isaacs equation; Hopf–Lax formula; Reach–Avoid set; Stochastic target game; 49K35; 49K45; 49L25; 49L20; 90C47 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13235-016-0183-5

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