Microarray techniques are used to generate a large amount of information on gene expression. This information can be statistically processed and analyzed to identify the genes useful for the diagnosis and prognosis of genetic diseases. Game theoretic tools are applied to analyze the gene expression data. Gene co-expression networks are increasingly used to explore the system-level functionality of genes, where the roles of the genes in building networks in addition to their independent activities are also considered. In this paper, we develop a novel microarray network game by constructing a gene co-expression network and defining a game on this network. The notion of the Link Relevance Index (LRI) for this network game is introduced and characterized. The LRI successfully identifies the relevant cancer biomarkers. It also enables identifying salient genes in the colon cancer dataset. Network games can more accurately describe the interactions among genes as their basic premises are to consider the interactions among players prescribed by a network structure. LRI presents a tool to identify the underlying salient genes involved in cancer or other metabolic syndromes.