From Centrality Discounts to Centrality Premia: Interoperability and Platform Competition in Social Networks

2026-07-10

AI Summary

This study investigates how interoperability shapes personalized pricing competition between platforms in social networks. The authors develop a duopoly model of differentiated platforms, where consumers derive network externalities from neighbors using the same or interoperable platforms. By integrating game theory, network economics, and the Katz–Bonacich centrality measure from graph theory, they derive closed-form equilibrium prices for arbitrary network structures. Their analysis reveals that whether central users receive discounts or premiums depends on the relative magnitude of interoperability and product substitutability. A critical threshold exists at which equilibrium prices become independent of users’ network positions. Furthermore, interoperability attenuates price competition between platforms, incentivizing them to favor denser user networks and reversing the conventional direction of price discrimination—whereby highly central users, who typically benefit under standard models, may instead face higher prices.

Abstract

We study how interoperability reshapes competitive price discrimination when consumers are embedded in a social network. Two differentiated platforms set personalized prices; consumers benefit from neighbors' consumption of the same platform and, under interoperability, of the rival. Equilibrium prices obtain in closed form for arbitrary networks and contain a network-position term, proportional to Katz-Bonacich centrality, whose sign is determined by whether interoperability exceeds product substitutability. Below this threshold, platforms contest central consumers and grant centrality discounts; above it, central consumers become gateways to a shared cross-platform network and pay premia; at the threshold, prices are independent of network position. Interoperability softens price competition, can make platforms favor denser consumer networks, and reverses which side of the market gains from price discrimination.

Problem

• interoperability
• platform competition
• price discrimination
• social networks
• Katz-Bonacich centrality

Innovation

• interoperability
• price discrimination
• social networks
• Katz-Bonacich centrality
• platform competition