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An encounter among a target, an intercepting missile and a defending missile is studied in a linear quadratic game setting. The purpose of the defending missile is to destroy the intercepting missile, before the latter reaches the target. The limiting values of the three participants optimal strategies is studied as the quadratic weight on the defending missiles acceleration command tends to zero. It is shown that in the limit the intercepting missiles and the targets optimal strategies are identical in form to that obtained in the game without the defending missile.