# Bounding the inefficiency of compromise in opinion formation

## TL;DR

This paper models opinion formation in social networks as strategic games where users compromise between personal beliefs and neighbors' opinions, analyzing how neighborhood size impacts the inefficiency of equilibria.

## Contribution

It introduces a game-theoretic framework for opinion formation with compromise and quantifies the inefficiency of equilibria based on neighborhood size.

## Key findings

- Inefficiency of equilibria increases with neighborhood size.
- Compromise incurs a significant cost in opinion dynamics.
- The model provides bounds on the price of anarchy in social opinion formation.

## Abstract

Social networks on the Internet have seen an enormous growth recently and play a crucial role in different aspects of today's life. They have facilitated information dissemination in ways that have been beneficial for their users but they are often used strategically in order to spread information that only serves the objectives of particular users. These properties have inspired a revision of classical opinion formation models from sociology using game-theoretic notions and tools. We follow the same modeling approach, focusing on scenarios where the opinion expressed by each user is a compromise between her internal belief and the opinions of a small number of neighbors among her social acquaintances. We formulate simple games that capture this behavior and quantify the inefficiency of equilibria using the well-known notion of the price of anarchy. Our results indicate that compromise comes at a cost that strongly depends on the neighborhood size.