A Survey on Hypergame Theory: Modeling Misaligned Perceptions and Nested Beliefs for Multi-agent Systems

TL;DR

This paper targets the gap between classical game theory and real-world multi-agent systems by focusing on hypergame theory, which captures misperceptions and nested beliefs through perceptual games. It provides a formal introduction to hypergame theory, including hierarchical hypergames and Hypergame Normal Form (HNF), and proposes agent-compatibility criteria and an agent-based classification framework. An extensive systematic review of $44$ agent-compatible studies maps domain usage, integration fidelity, and task focus, revealing a dominance of multi-level hypergames and graph-based models, especially in cybersecurity, while HNF remains underutilized outside that domain. The findings highlight structural gaps such as the lack of a universal agent-oriented hypergame language and opportunities to integrate hypergames with planning, epistemic reasoning, and human–AI interaction, offering a concrete roadmap for advancing realistic, misperception-aware MAS modeling. The work thus provides both a theoretical consolidation and a practical guide for applying hypergames to dynamic, human-centric, and adversarial MAS contexts.

Abstract

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 44 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.

Figures (14)

• Figure 1: Distribution of the evaluated 320 papers based on our selection criteria. The left chart illustrates the composition of papers eliminated due to irrelevance, duplication, or being written in a language other than English. The chart to the right illustrates the agent-compatibility evaluation that resulted in the final 44 papers considered for our review.
• Figure 2: Frequency of all hypergame-relevant and agentic publications over time.
• Figure 3: Publication counts per authors with at least 3 associated works.
• Figure 4: Distribution of model types. Hybrid models that span multiple categories are counted in each relevant type.
• Figure 5: Distribution of agent-compatible hypergame papers across high-level application domains and their associated sub-domains, where sum-domains can overlap between application domains.