This paper establishes an MPEC model by using infinitely many differentiated classes of customers equilibrium method to analyze price strategy and network-size allocation strategy for a two-sided monopoly platform taking into account the choice behaviour of vertical differential two-sided users. Considering the multiple market equilibria problem, suply curve and demand curve are applied to analyzing the geometric features and feasible region of the multiple equilibria. The optimal price strategies are derived under both optimistic and pesimistic preferences for the multiple equilibria problem. The optimal network-size allocation strategies are also derived under these two preferences and the duality for optimistic price strategy and network-size allocation strategy is evidenced. In order to provide helpful suggestions and references for platform companies, assuming an initial network-size, the limit solution of the network-size trajectory iterative equation for solving equilibrium fixed-point problem of two-sided platform users is studied, and the optimal price strategies for a given network sizes are obtained.