  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.
