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Techniques based on pursuit-evasion (PE) games are often applied in military operations of autonomous vehicles (AV) in the presence of mobile targets. Recently with increasing use of AVs, new scenarios emerge such as surveillance and persistent area denial. Compared with PE games, the actual roles of the pursuer and the evader have changed. In these emerging scenarios the evader acts as an intruder striking at some asset; at the same time the pursuer tries to destroy the intruder to protect the asset. Due to the presence of an asset, the PE game model with two sets of players (pursuers and evaders) is no longer adequate. We call this new problem a game of defending an asset(s) (DA). In this paper we study DA games under the framework of a linear quadratic (LQ) formulation. Three different DA games are addressed: 1) defending a stationary asset, 2) defending a moving asset with an arbitrary trajectory, and 3) defending an escaping asset. Equilibrium game strategies of the players are derived for each case. A repetitive scheme is proposed for implementation of the LQ strategies, and we demonstrate with simulations that the LQ strategies based on the repetitive implementation can provide good control guidance laws for DA games.