Endogenous Networks, Pricing Strategies, and State Regulation in Oligopolistic Markets: A Three-Stage Model with Eigenvector Centrality

This study presents a game-theoretic model of oligopolistic competition in digital markets, integrating endogenous network formation, varied pricing strategies, nonlinear demand, network externalities, and state regulation to analyze price differences. The model features a three-stage game where the state implements taxes and subsidies to maximize social welfare, producers invest in network connections, and set prices, some using consumer connection-based pricing. Consumers form connections based on prices, investments, and state incentives, creating scale-free networks. Through advanced mathematical methods, we prove a stable equilibrium, linking prices to a measure of network influence shaped by regulation. Simulations across various network structures, including a large-scale case with 50 producers, show that baseline regulation reduces price differences by about 28 % and increases welfare by up to 12 %. Further analysis reveals that stronger taxes and subsidies further decrease price variation by approximately 77 % and boost welfare by 15 %, guiding regulatory design. Aligned with the European Union’s Digital Markets Act and United States antitrust actions, this model provides strategic and policy insights for platform economies, advancing industrial organization and competition policy research. JEL: C72, D43, D85, L13, L51