This article discusses three models of two-sided markets, where two groups of agents interact via platforms. The key determinants of equilibrium prices are the magnitude of cross-group externalities, the basis of fees (lump-sum or per-transaction), and whether agents join one or multiple platforms. The first model considers a monopoly platform, where the platform's profit is influenced by cross-group externalities and the type of fee structure. The second model involves competing platforms where agents join a single platform, and the third model, termed "competitive bottlenecks," involves one group joining all platforms while the other group chooses platforms individually. In the monopoly platform model, the platform's profit is affected by the external benefits of attracting agents from the other group. The optimal prices are determined by balancing the cost of service and the external benefits. In the competing platforms model, the equilibrium prices depend on the interaction between the two groups and the differentiation parameters. The competitive bottleneck model highlights that platforms have monopoly power over the single-homing side, leading to higher prices for the multi-homing side. The article also discusses the effects of different tariff structures, such as fixed fees versus per-transaction charges, on platform profits and market outcomes. It compares these models with existing literature, including Caillaud and Jullien (2003) and Rochet and Tirole (2003), and highlights the differences in assumptions about agent utility, platform fees, and costs. The analysis shows that the structure of tariffs and costs significantly influences the equilibrium prices and market outcomes in two-sided markets.This article discusses three models of two-sided markets, where two groups of agents interact via platforms. The key determinants of equilibrium prices are the magnitude of cross-group externalities, the basis of fees (lump-sum or per-transaction), and whether agents join one or multiple platforms. The first model considers a monopoly platform, where the platform's profit is influenced by cross-group externalities and the type of fee structure. The second model involves competing platforms where agents join a single platform, and the third model, termed "competitive bottlenecks," involves one group joining all platforms while the other group chooses platforms individually. In the monopoly platform model, the platform's profit is affected by the external benefits of attracting agents from the other group. The optimal prices are determined by balancing the cost of service and the external benefits. In the competing platforms model, the equilibrium prices depend on the interaction between the two groups and the differentiation parameters. The competitive bottleneck model highlights that platforms have monopoly power over the single-homing side, leading to higher prices for the multi-homing side. The article also discusses the effects of different tariff structures, such as fixed fees versus per-transaction charges, on platform profits and market outcomes. It compares these models with existing literature, including Caillaud and Jullien (2003) and Rochet and Tirole (2003), and highlights the differences in assumptions about agent utility, platform fees, and costs. The analysis shows that the structure of tariffs and costs significantly influences the equilibrium prices and market outcomes in two-sided markets.