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.
IGTRVol7No3y2005001_Kumkov_Patsko_Shinar.pdf (3066 KB)
Kumkov S.S., Patsko V.S., Shinar J. On level sets with "narrow" throats in linear differential games // International Game Theory Review, Vol. 7, No. 3, September 2005. pp. 285–312.