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Paper Title: The Capture-the-Flag Differential Game: Attack, Transition and Retreat

Authors: Eloy Garcia and David W. Casbeer

The capture-the-flag game between an Attacker and a Defender is addressed in this paper as a two-phase differential game. A novel solution is provided where the two phases are connected by a transition phase. In such transition phase, the Defender evaluates the outcome of Phase I and, by realizing that the optimal play results in an unfavorable outcome, decides to transition to Phase II by determining the optimal starting position to intercept the Attacker in its way back to the safe zone.

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Different choices for the Transition Phase. a) D aims at F and it gives the opportunity to A to win Phase II as well. b) D takes a defensive position in order to intercept A before it can reach S.