Users' dynamics on digital platforms

We discuss novel methods for predicting and influencing dynamics of the volume of users on two-sided platforms. We study the strategies that make platforms more efficient. The new approach is based on dynamical systems techniques, and allows to model platforms with multiple types of users, i.e., allows natural generalization to multi-sided platforms. Study of the qualitative properties and asymptotics of dynamical system's trajectories helps to make conclusions about tendency of the platform. This is essential for our definition of payoff function, which reflects long term future benefits. Utilizing this definition of payoff, we introduce Nash basin of attraction. Inside of Nash basins of attraction the number of all types of users is growing and tends to the ('locally') highest payoff. These regions are beneficial for platform owners. They are also attractive for platform users, because their number is increasing. We demonstrate the theory with examples and provide simulations showing how these ideas can be used for practical tasks.