In this paper, we propose a game-theoretic tree matching algorithm for object detection in high resolution (HR) remotely sensed images, where, given a scene image and an object image, the goal is to determine whether or not the object exists in the scene image. To that effect, tree based representations of the images are obtained using a hierarchical scale space approach. The nodes of the tree denote regions in the image and edges represent the relative containment between different regions. Once we have the tree representations of each image, the task of object detection is reformulated as a tree matching problem. We propose a game-theoretic technique to search for the node correspondences between a pair of trees. This method involves defining a non-cooperative matching game, where strategies denote the possible pairs of matching regions and payoffs determine the compatibilities between these strategies. Trees are matched by finding the evolutionary stable states (ESS) of the game. To validate the effectiveness of the proposed algorithm, we perform experiments on both synthetic and HR remotely sensed images. Our results demonstrate the robustness of the tree representation with respect to different spatial variations of the images, as well as the effectiveness of the proposed game-theoretic tree matching algorithm.