ON LEVEL SETS WITH "NARROW THROATS" IN LINEAR DIFFERENTIAL GAMES

Sergey S. Kumkov (), Valery S. Patsko () and Josef Shinar ()
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Sergey S. Kumkov: Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str., 16, Ekaterinburg, 620219, Russia
Valery S. Patsko: Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str., 16, Ekaterinburg, 620219, Russia
Josef Shinar: Faculty of Aerospace Engineering, Technion — Israel Institution of Technology, Haifa, 32000, Israel

International Game Theory Review (IGTR), 2005, vol. 07, issue 03, 285-311

Abstract: Examples with zero-sum linear differential games of fixed terminal time and a convex terminal payoff function depending on two components of the phase vector are considered. Such games can have an indifferent zone with constant value function. The level set of the value function associated with the indifferent zone is called the "critical" tube. In the selected examples, the critical tube and the neighboring level sets exhibit "narrow throats". Presence of such throats requires extremely precise computations for constructing the level sets. The paper presents different forms of critical tubes with narrow throats and indicates the combinations of problem parameters that can produce them.

Keywords: Differential games; value function; level sets; numerical constructions (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0219198905000533

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