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

TL;DR

This survey reviews hypergame theory's role in modeling misperceptions and nested beliefs in multi-agent systems, highlighting its applications, limitations, and future research directions.

Contribution

It systematically analyzes 44 studies on hypergame theory, introduces an agent-based classification framework, and identifies gaps and opportunities for future research.

Findings

Hierarchical and graph-based models are prevalent in deceptive reasoning.

Limited adoption of HNF-based models and formal hypergame languages.

Opportunities exist for modeling human-agent and agent-agent misalignments.

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.