# A Geometric Embedding Approach to Multiple Games and Multiple Populations

arXiv: https://arxiv.org/abs/2401.05918 · HTML: https://mlsanity.com/paper/2401.05918/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2024.

## Built on by (most cited first, 6 of 6)

- [Generative Modeling of Discrete Joint Distributions by E-Geodesic Flow Matching on Assignment Manifolds](https://mlsanity.com/paper/2402.07846/) (2024)
- [Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data](https://mlsanity.com/paper/2406.04527/) (2024)
- [Fisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients](https://mlsanity.com/paper/2403.19448/) (2024)
- [Optimal Rates of Convergence for Entropy Regularization in Discounted Markov Decision Processes](https://mlsanity.com/paper/2406.04163/) (2024)
- [Sigma Flows for Image and Data Labeling and Learning Structured Prediction](https://mlsanity.com/paper/2408.15946/) (2024)
- [Riemannian Patch Assignment Gradient Flows](https://mlsanity.com/paper/2504.13024/) (2025)

## Abstract (arXiv)

This paper studies a meta-simplex concept and geometric embedding framework for multi-population replicator dynamics. Central results are two embedding theorems which constitute a formal reduction of multi-population replicator dynamics to single-population ones. In conjunction with a robust mathematical formalism, this provides a toolset for analyzing complex multi-population models. Our framework provides a unifying perspective on different population dynamics in the literature which in particular enables to establish a formal link between multi-population and multi-game dynamics.