Power in Sharing Networks with a priori Unions

2025-07-17

AI Summary

This paper addresses power allocation among firms competing and cooperating within a shared technological network featuring ex-ante coalitions. We propose a novel power index integrating degree centrality with rescaled eigenvector centrality, and—within the framework of transferable utility (TU) games on graphs—first axiomatize the Shapley value for technology licensing networks, thereby endowing the index with rigorous economic interpretation. Theoretically, we prove its monotonicity and axiom independence. Empirically, we find that the core of the associated TU game is empty for most networks, exposing intrinsic instability in technology-sharing mechanisms; furthermore, dominant firms’ structural positions remain robust under weak inter-sectoral technology spillovers. Our methodology unifies graph-theoretic modeling, centrality measurement, and a non-negative market-coefficient adjustment mechanism.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

We introduce and analyze a novel family of power indices tailored for sharing networks in technological markets, where firms operate competitively within, but not across, distinct industrial sectors. In these settings, inter-firm collaboration structures emerge from formal technology licensing agreements. The proposed indices are defined over graphs with a priori unions and combine two key centrality measures - degree-based and rescaled eigenvector centrality - modulated by positive market coefficients that reflect sectoral dynamics. We first explore the monotonicity properties of these indices, highlighting their responsiveness to local changes in network structure. Interestingly, major economic actors exhibit structural stability when inter-sectoral technological spillovers are minimal. Building on these findings, we provide theoretical underpinnings by characterizing the indices as the Shapley values of a family of coherent and economically interpretable transferable utility (TU) games defined over such graphs. However, for a broad class of network structures, the core of these TU games is often empty, signaling inherent instability in technological sharing arrangements. Finally, we offer an axiomatic foundation for this family of indices, proving independence of the proposed axioms. This axiomatization extends naturally to exchange networks, even when stage-propagation coefficients are not positive.

Problem

• Modeling power indices for firms in sector-specific sharing networks
• Analyzing stability of inter-firm collaboration via technology licensing
• Characterizing axiomatic foundations for network-based power indices

Innovation

• Graph-based power indices with unions
• Combined degree and eigenvector centrality
• Shapley values for TU games analysis