# Decomposition of games: some strategic considerations

arXiv: https://arxiv.org/abs/1901.06048 · HTML: https://mlsanity.com/paper/1901.06048/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2019.

## Built on by (most cited first, 5 of 5)

- [A geometric decomposition of finite games: Convergence vs. recurrence under exponential weights](https://mlsanity.com/paper/2405.07224/) (2024)
- [No-regret learning in harmonic games: Extrapolation in the face of conflicting interests](https://mlsanity.com/paper/2412.20203/) (2024)
- [Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games](https://mlsanity.com/paper/2510.04407/) (2025)
- [The impact of uncertainty on regularized learning in games](https://mlsanity.com/paper/2506.13286/) (2025)
- [On the Decomposition of Differential Game](https://mlsanity.com/paper/2411.03802/) (2024)

## Abstract (arXiv)

Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a game-theoretical point of view, for instance games obtained via transformations such as duplications of strategies or positive affine mappings of of payoffs. We show the need to define classes of decompositions to achieve commutativity of game transformations and decompositions.