Balanced Contributions in Networks and Games with Externalities

2026-04-15

AI Summary

This work proposes the first allocation rule—termed the BCE rule—for network cooperative games with externalities that uniquely satisfies both balanced contributions and component efficiency. By leveraging spanning tree constructions and cycle space analysis from graph theory, together with algebraic identities, the rule reduces the balancedness conditions on non-tree edges to subnetworks, thereby effectively addressing the constraints induced by externalities. In complete networks, the BCE rule reproduces the classical Myerson value from the setting without externalities, thus unifying existing results. Moreover, unlike the FCE rule, which disregards network topology, the BCE rule explicitly incorporates both graph structure and externality effects, demonstrating its superior capacity for their joint modeling.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

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
• Web Mining and Content Analysis: Models for Web evolution

Abstract

For networks with externalities, where each component's worth may depend on the full network structure, balanced contributions and fairness lead to distinct component-efficient allocation rules. We characterize the unique component-efficient allocation rule satisfying balanced contributions -- the BCE rule. Existence is the main challenge: balanced contributions must hold on every edge, but the construction uses only spanning-tree edges. A cycle-sum identity bridges this gap by reducing balanced contributions on non-tree edges to relations in proper subnetworks. The BCE rule coincides with the Myerson value for TU games and with its generalization by Jackson--Wolinsky for network games without externalities, it recovers the externality-free value on the complete network, and -- unlike the fairness-based FCE rule -- it does not reduce to a graph-free formula applied to the graph-restricted game.

Problem

• balanced contributions
• network externalities
• component-efficient allocation
• cooperative games
• Myerson value

Innovation

• balanced contributions
• component-efficient allocation
• cycle-sum identity
• network externalities
• BCE rule