# Bounds on the Price of Anarchy for a More General Class of Directed Graphs in Opinion Formation Games

arXiv: https://arxiv.org/abs/1602.02527 · HTML: https://mlsanity.com/paper/1602.02527/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2016.

## Built on by (most cited first, 3 of 3)

- [Dynamics and Convergences for Markov Coevolutionary Opinion Formation Games in Dynamic Social Networks](https://mlsanity.com/paper/2607.05580/) (2026)
- [Opinion Leader Detection in Online Social Networks Based on Output and Input Links](https://mlsanity.com/paper/2208.13161/) (2022)
- [Agent-based Modeling: Equilibrium, Echo Chambers, and Efficiency in Hybrid Coevolutionary Opinion Games](https://mlsanity.com/paper/2609.27639/) (2026)

## Abstract (arXiv)

In opinion formation games with directed graphs, a bounded price of anarchy is only known for weighted Eulerian graphs. Thus, we bound the price of anarchy for a more general class of directed graphs with conditions intuitively meaning that each node does not influence the others more than she is influenced, where the bounds depend on such difference (in a ratio). We also show that there exists an example just slightly violating the conditions with an unbounded price of anarchy.