# Finite composite games: Equilibria and dynamics

arXiv: https://arxiv.org/abs/1503.07935 · HTML: https://mlsanity.com/paper/1503.07935/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2015.

## Built on by (most cited first, 9 of 9)

- [Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback](https://mlsanity.com/paper/2112.02856/) (2021)
- [Asymptotic Convergence and Performance of Multi-Agent Q-Learning Dynamics](https://mlsanity.com/paper/2301.09619/) (2023)
- [Learning in nonatomic games, Part I: Finite action spaces and population games](https://mlsanity.com/paper/2107.01595/) (2021)
- [Adaptive, Doubly Optimal No-Regret Learning in Strongly Monotone and Exp-Concave Games with Gradient Feedback](https://mlsanity.com/paper/2310.14085/) (2023)
- [Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting](https://mlsanity.com/paper/2111.09982/) (2021)
- [On the Stability of Learning in Network Games with Many Players](https://mlsanity.com/paper/2403.15848/) (2024)
- [Convergence and Connectivity: Dynamics of Multi-Agent Q-Learning in Random Networks](https://mlsanity.com/paper/2503.10186/) (2025)
- [Stability of Multi-Agent Learning: Convergence in Network Games with Many Players](https://mlsanity.com/paper/2307.13922/) (2023)
- [Nested replicator dynamics, nested logit choice, and similarity-based learning](https://mlsanity.com/paper/2407.17815/) (2024)

## Abstract (arXiv)

We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable players. We recall and compare the basic properties, expressed through variational inequalities, concerning equilibria, potential games and dissipative games, as well as evolutionary dynamics. Then we consider composite games where the three categories of participants are present, a typical example being congestion games, and extend the previous properties of equilibria and dynamics. Finally we describe an instance of composite potential game.