# A Survey on Hypergame Theory: Modelling Misaligned Perceptions and Nested Beliefs for Multi-Agent Systems

arXiv: https://arxiv.org/abs/2507.19593 · HTML: https://mlsanity.com/paper/2507.19593/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 89 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 17 of 17)

- [Quantifying Misalignment Between Agents: Towards a Sociotechnical Understanding of Alignment](https://mlsanity.com/paper/2406.04231/) (2024)
- [Approximating Human Strategic Reasoning with LLM-Enhanced Recursive Reasoners Leveraging Multi-agent Hypergames](https://mlsanity.com/paper/2502.07443/) (2025)
- [Deceptive Labeling: Hypergames on Graphs for Stealthy Deception](https://mlsanity.com/paper/2004.05213/) (2020)
- [Decoy Allocation Games on Graphs with Temporal Logic Objectives](https://mlsanity.com/paper/2010.01208/) (2020)
- [Learning to Deceive in Multi-Agent Hidden Role Games](https://mlsanity.com/paper/2209.01551/) (2022)
- [Single-Leader-Multiple-Followers Stackelberg Security Game with Hypergame Framework](https://mlsanity.com/paper/2107.14625/) (2021)
- [Dynamic Hypergames for Synthesis of Deceptive Strategies with Temporal Logic Objectives](https://mlsanity.com/paper/2007.15726/) (2020)
- [I Know You Can't See Me: Dynamic Occlusion-Aware Safety Validation of Strategic Planners for Autonomous Vehicles Using Hypergames](https://mlsanity.com/paper/2109.09807/) (2021)
- [Dynamic Coalition Structure Detection in Natural Language-based Interactions](https://mlsanity.com/paper/2502.16339/) (2025)
- [The Influence of Human-inspired Agentic Sophistication in LLM-driven Strategic Reasoners](https://mlsanity.com/paper/2505.09396/) (2025)
- [A Theory of Hypergames on Graphs for Synthesizing Dynamic Cyber Defense with Deception](https://mlsanity.com/paper/2008.03210/) (2020)
- [Synthesis of Deceptive Strategies in Reachability Games with Action Misperception (Technical Report)](https://mlsanity.com/paper/2104.11676/) (2021)
- [Quantitative Planning with Action Deception in Concurrent Stochastic Games](https://mlsanity.com/paper/2301.01349/) (2023)
- [Integrated Resource Allocation and Strategy Synthesis in Safety Games on Graphs with Deception](https://mlsanity.com/paper/2407.14436/) (2024)
- [Opportunistic Synthesis in Reactive Games under Information Asymmetry](https://mlsanity.com/paper/1906.05847/) (2019)
- [Hypergame Theory for Decentralized Resource Allocation in Multi-user Semantic Communications](https://mlsanity.com/paper/2409.17985/) (2024)
- [Reactive Synthesis of Sensor Revealing Strategies in Hypergames on Graphs](https://mlsanity.com/paper/2412.01975/) (2024)

## Built on by (most cited first, 2 of 2)

- [Hypergame Rationalisability: Solving Agent Misalignment In Strategic Play](https://mlsanity.com/paper/2512.11942/) (2025)
- [Building Socio-Affective Artificial Intelligence for Interactive Multi-Agent Simulations](https://mlsanity.com/paper/2609.26927/) (2026)

## Abstract (arXiv)

Classical game-theoretic models typically assume rational agents, complete information, and common knowledge of payoffs - assumptions that are often violated in real-world MAS characterized by uncertainty, misaligned perceptions, and nested beliefs. To overcome these limitations, researchers have proposed extensions that incorporate models of cognitive constraints, subjective beliefs, and heterogeneous reasoning. Among these, hypergame theory extends the classical paradigm by explicitly modeling agents' subjective perceptions of the strategic scenario, known as perceptual games, in which agents may hold divergent beliefs about the structure, payoffs, or available actions. We present a systematic review of agent-compatible applications of hypergame theory, examining how its descriptive capabilities have been adapted to dynamic and interactive MAS contexts. We analyze 49 selected studies from cybersecurity, robotics, social simulation, communications, and general game-theoretic modeling. Building on a formal introduction to hypergame theory and its two major extensions - hierarchical hypergames and HNF - we develop agent-compatibility criteria and an agent-based classification framework to assess integration patterns and practical applicability. Our analysis reveals prevailing tendencies, including the prevalence of hierarchical and graph-based models in deceptive reasoning and the simplification of extensive theoretical frameworks in practical applications. We identify structural gaps, including the limited adoption of HNF-based models, the lack of formal hypergame languages, and unexplored opportunities for modeling human-agent and agent-agent misalignment. By synthesizing trends, challenges, and open research directions, this review provides a new roadmap for applying hypergame theory to enhance the realism and effectiveness of strategic modeling in dynamic multi-agent environments.