# Signed Network Formation Games and Clustering Balance

## TL;DR

This paper introduces a strategic model for signed network formation where individuals change relationships to reduce cognitive dissonance, leading to stable cluster configurations that extend previous models.

## Contribution

It presents a novel game-theoretic model that generates a wider variety of signed networks and characterizes dynamics toward sociologically meaningful clustering balance.

## Key findings

- The model converges to clustering balance configurations.
- It generalizes previous models to produce multiple clusters.
- The dynamics are characterized mathematically.

## Abstract

We propose a signed network formation game, in which pairs of individuals strategically change the signs of the edges in a complete network. These individuals are members of a social network who strategically reduce cognitive dissonances by changing their interpersonal appraisals. We characterize the best-response dynamics for this game and prove that its implementation \pc{can} dynamically drive the network to a sociologically meaningful sign configuration called clustering balance. In this configuration, agents in the social network form one or more clusters that have positive relationships among their members but negative relationships among members of other clusters. In the past, various researchers in the fields of psycho-sociology, political science, and physics have looked at models that explain the generation of up to two clusters. Our work contributes to these fields by proposing a simple model that generates a broader class of signed networks.