This study proposes two novel deterministic transition models of a belief and a Bayesian Nash equilibrium (BNE) for static Bayesian games. The transition models can be obtained from the Karush-Kuhn-Tucker condition, and as a result, they are expressed in a discrete-time time-varying autonomous system in the state-space representation that expresses evolution of the belief and the BNE. As well, this study analytically checks stability of the models. A contribution of this study is to make it possible to apply our model-based fashions to analysis and design problems related to the Bayesian game.