Feature matching is a fundamental problem in computer vision. Compared with graph matching, hypergraph matching is able to encode more invariance between correspondences. Different from the majority of existing hypergraph matching algorithms, a game-theoretic algorithm has been developed by transforming hypergraph matching to hypergraph clustering, which is then solved within the framework of a non-cooperative multi-player clustering game. This algorithm obtains the final matches as a cluster of consistent candidate matches and has high accuracy and robustness to outliers in comparison with other competitors. However, in further works we find that this algorithm tends to generate a small number of matches, and the increase of number of matches can only be obtained at the cost of a huge computation load. Our investigation of the algorithm shows that it has a large requirement of internal similarity in a cluster, and therefore generates small clusters of high density. This motivates us to expand the cluster so that more candidate matches are accepted as final matches. For this purpose, we define the density of vertices in a hypergraph and expand the cluster based on relative density relationship among the vertices. In matching experiments with both synthetic and real datasets, our algorithm is shown to generate the same number of or more matches with much less running time in comparison with the original algorithm. Meanwhile, it preserves the advantage of high accuracy and robustness to outlier in comparison with some competitors.