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This paper is concerned with the effect of capacity constraints on the locations of terror response facilities. We assume that the state has limited resources, and multiple facilities may be involved in the response until the demand is satisfied consequently. We formulate a leader-follower game model between the state and the terrorist and prove the existence and uniqueness of the Nash equilibrium. An integer linear programming is proposed to obtain the equilibrium results when the facility number is fixed. The problem is demonstrated by a case study of the 19 districts of Shanghai, China.