A simplified mathematical model for two-sided market systems with an intervening engineered platform

A two-sided market involves two different user groups whose interactions are enabled over a platform that provides a distinct set of values to either side. In such market systems, one side's participation depends on the value created by presence of the other side over the platform. Two-sided market platforms must acquire enough users on both sides in appropriate proportions to generate value to either side of the user market. In this paper, we present a simplified, generic mathematical model for two-sided markets with an intervening platform that enables interaction between the two different sets of users with distinct value propositions. The proposed model captures both the same side as well as cross-side effects (i.e., network externalities) and can capture any behavioral asymmetry between the different sides of the two-sided market system. The cross-side effects are captured using the notion of affinity curves while same side effects are captured using four rate parameters. We demonstrate the methodology on canonical affinity curves and comment on the attainment of stability at the equilibrium points of two-sided market systems. Subsequently a stochastic choice-based model of consumers and developers is described to simulate a two-sided market from grounds-up and the observed affinity curves are documented. Finally we discuss how the two-sided market model links with and impacts the engineering characteristics of the platform.