# Learning Parametric Closed-Loop Policies for Markov Potential Games

arXiv: https://arxiv.org/abs/1802.00899 · HTML: https://mlsanity.com/paper/1802.00899/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2018.

## Built on by (most cited first, 21 of 21)

- [Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games](https://mlsanity.com/paper/2106.01969/) (2021)
- [When Can We Learn General-Sum Markov Games with a Large Number of Players Sample-Efficiently?](https://mlsanity.com/paper/2110.04184/) (2021)
- [Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence](https://mlsanity.com/paper/2202.04129/) (2022)
- [On Improving Model-Free Algorithms for Decentralized Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2110.05707/) (2021)
- [Independent and Decentralized Learning in Markov Potential Games](https://mlsanity.com/paper/2205.14590/) (2022)
- [Provably Fast Convergence of Independent Natural Policy Gradient for Markov Potential Games](https://mlsanity.com/paper/2310.09727/) (2023)
- [Learning in Congestion Games with Bandit Feedback](https://mlsanity.com/paper/2206.01880/) (2022)
- [Independent Learning in Constrained Markov Potential Games](https://mlsanity.com/paper/2402.17885/) (2024)
- [Learning to Shape Rewards using a Game of Two Partners](https://mlsanity.com/paper/2103.09159/) (2021)
- [Convergence Rates for Localized Actor-Critic in Networked Markov Potential Games](https://mlsanity.com/paper/2303.04865/) (2023)
- [Learning Stationary Nash Equilibrium Policies in n-Player Stochastic Games with Independent Chains](https://mlsanity.com/paper/2201.12224/) (2022)
- [Convergence and Price of Anarchy Guarantees of the Softmax Policy Gradient in Markov Potential Games](https://mlsanity.com/paper/2206.07642/) (2022)
- [Efficiently Computing Nash Equilibria in Adversarial Team Markov Games](https://mlsanity.com/paper/2208.02204/) (2022)
- [Markov α-Potential Games](https://mlsanity.com/paper/2305.12553/) (2023)
- [Learning Distributed and Fair Policies for Network Load Balancing as Markov Potential Game](https://mlsanity.com/paper/2206.01451/) (2022)
- [Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property](https://mlsanity.com/paper/2312.12067/) (2023)
- [DPMAC: Differentially Private Communication for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2308.09902/) (2023)
- [Scalable and Independent Learning of Nash Equilibrium Policies in n-Player Stochastic Games with Unknown Independent Chains](https://mlsanity.com/paper/2312.01587/) (2023)
- [Independent Learning of Nash Equilibria in Partially Observable Markov Potential Games with Decoupled Dynamics](https://mlsanity.com/paper/2605.06377/) (2026)
- [Almost Sure Convergence of Networked Policy Gradient over Time-Varying Networks in Markov Potential Games](https://mlsanity.com/paper/2410.20075/) (2024)
- [Reinforcement Learning: From Algorithms To Foundation Models](https://mlsanity.com/paper/2607.17560/) (2026)

## Abstract (arXiv)

Multiagent systems where agents interact among themselves and with a stochastic environment can be formalized as stochastic games. We study a subclass named Markov potential games (MPGs) that appear often in economic and engineering applications when the agents share a common resource. We consider MPGs with continuous state-action variables, coupled constraints and nonconvex rewards. Previous analysis followed a variational approach that is only valid for very simple cases (convex rewards, invertible dynamics, and no coupled constraints); or considered deterministic dynamics and provided open-loop (OL) analysis, studying strategies that consist in predefined action sequences, which are not optimal for stochastic environments. We present a closed-loop (CL) analysis for MPGs and consider parametric policies that depend on the current state. We provide easily verifiable, sufficient and necessary conditions for a stochastic game to be an MPG, even for complex parametric functions (e.g., deep neural networks); and show that a closed-loop Nash equilibrium (NE) can be found (or at least approximated) by solving a related optimal control problem (OCP). This is useful since solving an OCP--which is a single-objective problem--is usually much simpler than solving the original set of coupled OCPs that form the game--which is a multiobjective control problem. This is a considerable improvement over the previously standard approach for the CL analysis of MPGs, which gives no approximate solution if no NE belongs to the chosen parametric family, and which is practical only for simple parametric forms. We illustrate the theoretical contributions with an example by applying our approach to a noncooperative communications engineering game. We then solve the game with a deep reinforcement learning algorithm that learns policies that closely approximates an exact variational NE of the game.