语法修改：Without loss of generality each player is labeled with index 1 to n and assigned to all clusters which means that cluster i contains a sequence of intelligences from 1 to m eg cluster 1 contains

Without loss of generality, let each player be labeled with an index from 1 to n and assigned to all clusters. This implies that cluster i contains a sequence of intelligences from 1 to m, for example, cluster 1 contains intelligences labeled 1-n.