On Signed Network Coordination Games

2025-05-14

AI Summary

This paper investigates binary-action network games on signed directed graphs featuring both cooperative and antagonistic interactions, focusing on the existence and stability of Nash equilibria when a structurally “cohesive” subgroup of players exists. Methodologically, it pioneers the integration of structural balance theory with graph cohesion concepts to formulate a utility aggregation model that incorporates individual preferences and weighted edge signs; equilibrium properties are then analyzed via supermodular game theory and best-response dynamics. The main contributions are: (i) a rigorous proof that consensus or bipolarization constitute the only two types of stable Nash equilibria attainable within the cohesive subgroup, both dynamically stable; and (ii) an extension of supermodular game robustness theory, yielding a novel analytical framework for opinion evolution in social networks—one that combines structural interpretability with mathematical rigor.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• 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

Abstract

We study binary-action pairwise-separable network games that encompass both coordinating and anti-coordinating behaviors. Our model is grounded in an underlying directed signed graph, where each link is associated with a weight that describes the strenght and nature of the interaction. The utility for each agent is an aggregation of pairwise terms determined by the weights of the signed graph in addition to an individual bias term. We consider a scenario that assumes the presence of a prominent 'cohesive' subset of players, who are either connected exclusively by positive weights, or forms a structurally balanced subset that can be bipartitioned into two adversarial subcommunities with positive intra-community and negative inter-community edges. Given the properties of the game restricted to the remaining players, our results guarantee the existence of Nash equilibria characterized by a consensus or, respectively, a polarization within the first group, as well as their stability under best response transitions. Our results can be interpreted as robustness results, building on the supermodular properties of coordination games and on a novel use of the concept of graph cohesiveness.

Problem

• Study binary-action games with coordinating and anti-coordinating behaviors
• Analyze Nash equilibria in signed networks with cohesive player subsets
• Ensure stability of consensus or polarization under best response dynamics

Innovation

• Binary-action pairwise-separable network games
• Directed signed graph with weighted interactions
• Cohesive subset ensures Nash equilibria stability