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Detailed Proof of Existence of Value Function in Time-Optimal Games with Lifeline

Author

Listed:
  • Nataly V. Munts

    (Krasovskii Institute of Mathematics and Mechanics, UrB RAS, Yekaterinburg, Sverdlovsk Region, Russia)

  • Sergey S. Kumkov

    (Krasovskii Institute of Mathematics and Mechanics, UrB RAS, Yekaterinburg, Sverdlovsk Region, Russia)

Abstract

The paper discusses the existence of the value function of a time-optimal differential game with lifeline in a quite general formulation. In such a game, the first player tries to lead the trajectory of the system to a terminal set as soon as possible avoiding the lifeline. The aim of the second player is to lead the trajectory to the lifeline or, if it is not possible, to keep it outside the terminal set, or, if the latter is impossible too, to postpone maximally reaching the terminal set.

Suggested Citation

  • Nataly V. Munts & Sergey S. Kumkov, 2022. "Detailed Proof of Existence of Value Function in Time-Optimal Games with Lifeline," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 1-18, December.
    • Handle: RePEc:wsi:igtrxx:v:24:y:2022:i:04:n:s0219198922500141
    DOI: 10.1142/S0219198922500141
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