# Principal Trade-off Analysis

arXiv: https://arxiv.org/abs/2206.07520 · HTML: https://mlsanity.com/paper/2206.07520/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 57 references that are in the map.
- First posted on arXiv 9 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [OpenSpiel: A Framework for Reinforcement Learning in Games](https://mlsanity.com/paper/1908.09453/) (2019)
- [Deep Reinforcement Learning from Self-Play in Imperfect-Information Games](https://mlsanity.com/paper/1603.01121/) (2016)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [Open-ended Learning in Symmetric Zero-sum Games](https://mlsanity.com/paper/1901.08106/) (2019)
- [AI-GAs: AI-generating algorithms, an alternate paradigm for producing general artificial intelligence](https://mlsanity.com/paper/1905.10985/) (2019)
- [Real World Games Look Like Spinning Tops](https://mlsanity.com/paper/2004.09468/) (2020)
- [Re-evaluating Evaluation](https://mlsanity.com/paper/1806.02643/) (2018)
- [Pick Your Battles: Interaction Graphs as Population-Level Objectives for Strategic Diversity](https://mlsanity.com/paper/2110.04041/) (2021)
- [A Generalised Method for Empirical Game Theoretic Analysis](https://mlsanity.com/paper/1803.06376/) (2018)
- [An application of incomplete pairwise comparison matrices for ranking top tennis players](https://mlsanity.com/paper/1611.00538/) (2016)
- [Nonconvex Matrix Completion with Linearly Parameterized Factors](https://mlsanity.com/paper/2003.13153/) (2020)

## Abstract (arXiv)

How are the advantage relations between a set of agents playing a game organized and how do they reflect the structure of the game? In this paper, we illustrate "Principal Trade-off Analysis" (PTA), a decomposition method that embeds games into a low-dimensional feature space. We argue that the embeddings are more revealing than previously demonstrated by developing an analogy to Principal Component Analysis (PCA). PTA represents an arbitrary two-player zero-sum game as the weighted sum of pairs of orthogonal 2D feature planes. We show that the feature planes represent unique strategic trade-offs and truncation of the sequence provides insightful model reduction. We demonstrate the validity of PTA on a quartet of games (Kuhn poker, RPS+2, Blotto, and Pokemon). In Kuhn poker, PTA clearly identifies the trade-off between bluffing and calling. In Blotto, PTA identifies game symmetries, and specifies strategic trade-offs associated with distinct win conditions. These symmetries reveal limitations of PTA unaddressed in previous work. For Pokemon, PTA recovers clusters that naturally correspond to Pokemon types, correctly identifies the designed trade-off between those types, and discovers a rock-paper-scissor (RPS) cycle in the Pokemon generation type - all absent any specific information except game outcomes.