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This paper deals with the alternative mathematical modeling of the two-side platform. Two-sided platforms are specific multi-sided platforms that bring together two distinct groups of a model. The stochastic modeling by adapting various innovative mathematical methods including the first exceed theory and the stochastic pseudo-game theory has been applied for describing a two-sided platform more properly. A stochastic pseudo-game model is newly introduced to solve the two-sided platform more effectively. Analytically tractable results for operation thresholds for maximizing profits are provided and it also delivers the optimal balance of a two-sided platform. The paper includes how these innovative models are applied into various two-sided market situations. Additionally, users could conduct these multi-sided models to real business developments and the case practices of these unique models shall help the readers who want to find recommendations of their business situations easily even without having any mathematical background.