The Z-number is the most general representation of real-life information with reliability, and it also exhibits the highest descriptive power from the perspective of human cognition. This study focuses on the development of a computationally simple and effective Z-number model to address game problems by systematically comparing pairwise strategies derived from different players. The processing of Z-numbers requires computing fuzzy and probabilistic uncertainties; then, the cloud model is suggested to handle bimodal restriction in Z-numbers. In this manner, a novel concept of asymmetric normal Z-value (ANZ) is proposed. Subsequently, the concordance/discordance index and outranking relations of ANZs are suggested based on classic outranking rules. Next, an innovative game model is established by modeling the outranking relations of strategies of different players under multiple criteria. Finally, an illustrative example concerning enterprise market competition is provided to demonstrate the established model.