Competition and Collusion in Two-Sided Markets with an Outside Option

2025-05-09

AI Summary

This paper examines the equilibrium effects of competition and collusion in two-sided markets with external options. Method: We develop the first unified game-theoretic model integrating external options, platform count, and cross-side network effects; analyze Nash and collusive equilibria; and apply comparative statics to characterize how external option utility affects pricing, consumer surplus, and participation rates. Contribution/Results: We identify three key findings: (i) under weak cross-side network effects, collusion reduces both social welfare and participation—contrary to conventional wisdom; (ii) omitting external options systematically biases price and surplus estimates; and (iii) platform proliferation exhibits a critical threshold: beyond it, equilibrium prices decline while platform profits paradoxically rise. These results provide theoretically grounded, quantifiable criteria for platform regulation and antitrust policy design.

Technology Category

• Game Theory and Economic Paradigms: Coordination and Collaboration
• Multiagent Systems: Mechanism Design
• Search and Optimization: Other Foundations of Search & Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We introduce pricing formulas for competition and collusion models of two-sided markets with an outside option. For the competition model, we find conditions under which prices and consumer surplus may increase or decrease if the outside option utility increases. Therefore, neglecting the outside option can lead to either overestimation or underestimation of these equilibrium outputs. Comparing collusion to competition, we find that in cases of small cross-side externalities, collusion results in decreased normalized net deterministic utilities, reduced market participation and increased price, on both sides of the market. Additionally, we observe that as the number of platforms increases in the competition model, market participation rises. Profits, however, decrease when the net normalized deterministic utility is sufficiently low but increase when it is high. Furthermore, we identify specific conditions that quantify the change of price and consumer surplus when the competition increases.

Problem

• Analyze pricing in two-sided markets with outside options
• Compare competition vs collusion impacts on market outcomes
• Study platform count effects on participation and profits

Innovation

• Introduces pricing formulas for two-sided markets
• Analyzes competition and collusion impacts on prices
• Quantifies conditions for price and surplus changes