This paper formulates a support time game arising in one-on-one air combat with medium range air-to-air missiles. The game model provides game optimal support times of the missiles that can receive target information from the launching aircraft for selectable support times. The payoffs of the game are formulated as a weighted sum of the probabilities of hit to the adversary and own survival. Under suitable simplifying assumptions, a Nash equilibrium of the game can be computed by an iterative search involving a series of optimal control problems. For practical situations, an approximate real time computation scheme is introduced. The constructed model and the scheme are illustrated by numerical examples.
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