On Signed Network Coordination Games

TL;DR

This paper analyzes binary-action network games with signed graphs, establishing conditions for Nash equilibria characterized by consensus or polarization, and demonstrating their stability and robustness based on graph properties.

Contribution

It introduces a model for signed network games incorporating both coordination and anti-coordination, and provides new theoretical guarantees for equilibrium existence and stability.

Findings

Existence of Nash equilibria with consensus or polarization.

Stability of equilibria under best response dynamics.

Robustness results based on graph cohesiveness.

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.