Dynamics of two-sided markets

This paper considers a dynamical system, which models a two-sided market. I evaluate the volume of users from each side of the market as a function of time. I formulate and prove theorems describing the long-term behavior and tendency of the market. Even though I consider generic attachment functions, I obtain a concrete result, formulated in terms of properties of attachment functions. I conclude the paper with examples (defined by the most popular in economics attachment functions), which illustrate behavior of the two-sided markets. I also simulate some two-sided market scenarios, showing how adjustments of attachment functions can influence the users’ dynamics. Since platforms revenue depends on the number of users, this dynamical systems helps to analyze revenue over time. The dynamical system’s approach to the study of two-sided market problem allows natural generalization to multi-sided market, where one can utilize the same technique and obtain similar results in higher dimensions.