A differential game of pursuit and evasion on the real line is discussed with one pursuer and two evaders, the motion of the players being affected by noise. The game of degree is considered, where the pursuer strives to maximize the probability of his winning the game, i.e., of capturing at least one of the evaders, the probability function being given as a solution to a certain partial differential equation; the heat conduction analogy is also being discussed. The degenerate situation here arises in a natural way, and it is possible to present a quite detailed analysis of this case.
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This work was partially supported by a grant from Control Data.
Communicated by G. Leitmann
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Pachter, M., Yavin, Y. One pursuer and two evaders on the line: A stochastic pursuit-evasion differential game. J Optim Theory Appl 39, 513–539 (1983). https://doi.org/10.1007/BF00933756
- Stochastic differential games
- degenerate parabolic partial differential equations
- convective heat conduction