Dynamic Platform Competition 'In' and 'For' the Market

In many industries, platforms compete with incumbents that are open to all consumers, whereas platforms require user affiliation. Consequently, platforms face two layers of competition: for the market, to attract users, and in the market, to compete with incumbents. We develop a dynamic model integrating these layers, showing that as platform affiliation grows, in the market competition intensifies, pushing incumbents toward more aggressive pricing. Conversely, for the market competition diminishes, reducing the platform's incentive to compete aggressively. This interplay generates dynamic pricing behavior that can be non-monotonic over time, capturing the shifting incentives driving platform-incumbent competition across both dimensions.