# Abstracting Imperfect Information Away from Two-Player Zero-Sum Games

arXiv: https://arxiv.org/abs/2301.09159 · HTML: https://mlsanity.com/paper/2301.09159/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 67 references that are in the map.
- First posted on arXiv 22 Jan 2023.

## Builds on (most cited first, 29 of 29)

- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [The Hanabi Challenge: A New Frontier for AI Research](https://mlsanity.com/paper/1902.00506/) (2019)
- [Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learning](https://mlsanity.com/paper/2206.15378/) (2022)
- [Combining Deep Reinforcement Learning and Search for Imperfect-Information Games](https://mlsanity.com/paper/2007.13544/) (2020)
- [Bayesian Action Decoder for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1811.01458/) (2018)
- [A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games](https://mlsanity.com/paper/2206.05825/) (2022)
- [Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization](https://mlsanity.com/paper/2105.15186/) (2021)
- [From Poincar'e Recurrence to Convergence in Imperfect Information Games: Finding Equilibrium via Regularization](https://mlsanity.com/paper/2002.08456/) (2020)
- [Safe and Nested Subgame Solving for Imperfect-Information Games](https://mlsanity.com/paper/1705.02955/) (2017)
- [Rethinking Formal Models of Partially Observable Multiagent Decision Making](https://mlsanity.com/paper/1906.11110/) (2019)
- [Improving Policies via Search in Cooperative Partially Observable Games](https://mlsanity.com/paper/1912.02318/) (2019)
- [Solving Imperfect Information Games Using Decomposition](https://mlsanity.com/paper/1303.4441/) (2013)
- [Depth-Limited Solving for Imperfect-Information Games](https://mlsanity.com/paper/1805.08195/) (2018)
- [Scalable Online Planning via Reinforcement Learning Fine-Tuning](https://mlsanity.com/paper/2109.15316/) (2021)
- [Regularized Gradient Descent Ascent for Two-Player Zero-Sum Markov Games](https://mlsanity.com/paper/2205.13746/) (2022)
- [Solving Common-Payoff Games with Approximate Policy Iteration](https://mlsanity.com/paper/2101.04237/) (2021)
- [Unlocking the Potential of Deep Counterfactual Value Networks](https://mlsanity.com/paper/2007.10442/) (2020)
- [Common Information based Approximate State Representations in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2110.12603/) (2021)
- [HSVI can solve zero-sum Partially Observable Stochastic Games](https://mlsanity.com/paper/2210.14640/) (2022)
- [Timeability of Extensive-Form Games](https://mlsanity.com/paper/1502.03430/) (2015)
- [A Marriage between Adversarial Team Games and 2-player Games: Enabling Abstractions, No-regret Learning, and Subgame Solving](https://mlsanity.com/paper/2206.09161/) (2022)
- [Structure in the Value Function of Two-Player Zero-Sum Games of Incomplete Information](https://mlsanity.com/paper/1606.06888/) (2016)
- [Online Planning for Decentralized Stochastic Control with Partial History Sharing](https://mlsanity.com/paper/1908.02357/) (2019)
- [Team Optimal Control of Coupled Subsystems with Mean-Field Sharing](https://mlsanity.com/paper/2012.01418/) (2020)
- [Public Information Representation for Adversarial Team Games](https://mlsanity.com/paper/2201.10377/) (2022)
- [Structural Results and Explicit Solution for Two-Player LQG Systems on a Finite Time Horizon](https://mlsanity.com/paper/1303.3256/) (2013)
- [On Bellman's Optimality Principle for zs-POSGs](https://mlsanity.com/paper/2006.16395/) (2020)
- [HSVI for zs-POSGs using Concavity, Convexity and Lipschitz Properties](https://mlsanity.com/paper/2110.14529/) (2021)

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

- [Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4](https://mlsanity.com/paper/2309.17277/) (2023)
- [Scalable Decision Making for Games of Imperfect Information](https://mlsanity.com/paper/2511.07312/) (2025)
- [Detecting Multi-Agent Collusion Through Multi-Agent Interpretability](https://mlsanity.com/paper/2604.01151/) (2026)
- [The Update-Equivalence Framework for Decision-Time Planning](https://mlsanity.com/paper/2304.13138/) (2023)
- [Look-ahead Reasoning with a Learned Model in Imperfect Information Games](https://mlsanity.com/paper/2510.05048/) (2025)
- [ε-Optimally Solving Zero-Sum POSGs](https://mlsanity.com/paper/2406.00054/) (2024)

## Abstract (arXiv)

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and decision-time planning algorithms for common-payoff games. Unfortunately, a naive application of the same insight to two-player zero-sum games fails because Nash equilibria of the game with public policy announcements may not correspond to Nash equilibria of the original game. As a consequence, existing sound decision-time planning algorithms require complicated additional mechanisms that have unappealing properties. The main contribution of this work is showing that certain regularized equilibria do not possess the aforementioned non-correspondence problem -- thus, computing them can be treated as perfect-information problems. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective to solving two-player zero-sum games and yields a simplified framework for decision-time planning in two-player zero-sum games, void of the unappealing properties that plague existing decision-time planning approaches.