# Game Theoretic Rating in N-player general-sum games with Equilibria

arXiv: https://arxiv.org/abs/2210.02205 · HTML: https://mlsanity.com/paper/2210.02205/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 57 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 25 of 25)

- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
- [Human-level performance in first-person multiplayer games with population-based deep reinforcement learning](https://mlsanity.com/paper/1807.01281/) (2018)
- [OpenSpiel: A Framework for Reinforcement Learning in Games](https://mlsanity.com/paper/1908.09453/) (2019)
- [A Survey and Critique of Multiagent Deep Reinforcement Learning](https://mlsanity.com/paper/1810.05587/) (2018)
- [Deep Reinforcement Learning from Self-Play in Imperfect-Information Games](https://mlsanity.com/paper/1603.01121/) (2016)
- [Emergent Complexity via Multi-Agent Competition](https://mlsanity.com/paper/1710.03748/) (2017)
- [Open-ended Learning in Symmetric Zero-sum Games](https://mlsanity.com/paper/1901.08106/) (2019)
- [A Survey of Learning in Multiagent Environments: Dealing with Non-Stationarity](https://mlsanity.com/paper/1707.09183/) (2017)
- [Real World Games Look Like Spinning Tops](https://mlsanity.com/paper/2004.09468/) (2020)
- [Autocurricula and the Emergence of Innovation from Social Interaction: A Manifesto for Multi-Agent Intelligence Research](https://mlsanity.com/paper/1903.00742/) (2019)
- [A Generalized Training Approach for Multiagent Learning](https://mlsanity.com/paper/1909.12823/) (2019)
- [α-Rank: Multi-Agent Evaluation by Evolution](https://mlsanity.com/paper/1903.01373/) (2019)
- [Re-evaluating Evaluation](https://mlsanity.com/paper/1806.02643/) (2018)
- [EigenGame: PCA as a Nash Equilibrium](https://mlsanity.com/paper/2010.00554/) (2020)
- [Actor-Critic Policy Optimization in Partially Observable Multiagent Environments](https://mlsanity.com/paper/1810.09026/) (2018)
- [Learning to Play No-Press Diplomacy with Best Response Policy Iteration](https://mlsanity.com/paper/2006.04635/) (2020)
- [Correlation in Extensive-Form Games: Saddle-Point Formulation and Benchmarks](https://mlsanity.com/paper/1905.12564/) (2019)
- [Multi-Agent Training beyond Zero-Sum with Correlated Equilibrium Meta-Solvers](https://mlsanity.com/paper/2106.09435/) (2021)
- [Coarse Correlation in Extensive-Form Games](https://mlsanity.com/paper/1908.09893/) (2019)
- [Multiagent Evaluation under Incomplete Information](https://mlsanity.com/paper/1909.09849/) (2019)
- [Sample-based Approximation of Nash in Large Many-Player Games via Gradient Descent](https://mlsanity.com/paper/2106.01285/) (2021)
- [Estimating α-Rank by Maximizing Information Gain](https://mlsanity.com/paper/2101.09178/) (2021)

## Built on by (most cited first, 3 of 3)

- [Evaluating Agents using Social Choice Theory](https://mlsanity.com/paper/2312.03121/) (2023)
- [Re-evaluating Open-ended Evaluation of Large Language Models](https://mlsanity.com/paper/2502.20170/) (2025)
- [Combining Tree-Search, Generative Models, and Nash Bargaining Concepts in Game-Theoretic Reinforcement Learning](https://mlsanity.com/paper/2302.00797/) (2023)

## Abstract (arXiv)

Rating strategies in a game is an important area of research in game theory and artificial intelligence, and can be applied to any real-world competitive or cooperative setting. Traditionally, only transitive dependencies between strategies have been used to rate strategies (e.g. Elo), however recent work has expanded ratings to utilize game theoretic solutions to better rate strategies in non-transitive games. This work generalizes these ideas and proposes novel algorithms suitable for N-player, general-sum rating of strategies in normal-form games according to the payoff rating system. This enables well-established solution concepts, such as equilibria, to be leveraged to efficiently rate strategies in games with complex strategic interactions, which arise in multiagent training and real-world interactions between many agents. We empirically validate our methods on real world normal-form data (Premier League) and multiagent reinforcement learning agent evaluation.