# Preference graphs: a combinatorial tool for game theory

arXiv: https://arxiv.org/abs/2502.03546 · HTML: https://mlsanity.com/paper/2502.03546/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2025.

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

- [What preferences can - and cannot - predict in multi-agent online learning](https://mlsanity.com/paper/2608.13810/) (2026)
- [Sink equilibria and the attractors of learning in games](https://mlsanity.com/paper/2502.07975/) (2025)
- [Learning in Continuous Games from Pairwise Preference Feedback](https://mlsanity.com/paper/2610.05428/) (2026)

## Abstract (arXiv)

The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation indicates the preferred choice for that player. We show that the preference graph is a surprisingly fundamental tool for studying normal-form games, which arises from natural axioms and which underlies many key game-theoretic concepts, including dominated strategies and strict Nash equilibria, as well as classes of games like potential games, supermodular games and weakly acyclic games. The preference graph is especially related to game dynamics, playing a significant role in the behaviour of fictitious play and the replicator dynamic. Overall, we aim to equip game theorists with the tools and understanding to apply the preference graph to new problems in game theory.