Ontology of Wargames: Methods & Applications

• Wargames ontology is a formal framework that defines key structural elements, taxonomies, and simulation models to analyze complex conflict dynamics.
• It integrates rigorous mathematical models, game-theoretic principles, and multi-agent decision-making methods to support strategic simulations.
• Emerging AI techniques, including deep reinforcement learning and large language models, enhance automation and improve outcome analysis in wargame scenarios.

Wargames are structured, multi-agent simulations designed to explore and analyze conflict dynamics, strategic decision-making, and emergent behavior in adversarial, competitive, or cooperative scenarios. The ontology of wargames formalizes their constitutive elements, taxonomic distinctions, and methodological underpinnings, enabling precise classification, analysis, and automation across military, policy, entertainment, and cyber-physical domains. Recent works deploy mathematical modeling, AI, LLMs, and simulation frameworks to deepen this ontology, facilitating both analytical rigor and creative exploration.

1. Formal Taxonomy and Structural Elements

Wargames encompass a broad class of decision-making games, including military simulations, cyber defense contests, tabletop strategy games, and open-ended narrative scenarios (Hogan et al., 17 Apr 2024). The structural ontology of wargames is defined by several hierarchical and typological axes:

• Underlying Game System (UGS): Encodes the abstract rules and mechanics independent of presentation, typically formalized as $$\mathcal{G} = \langle \mathcal{P},\, \mathcal{T},\, \mathcal{S}_0,\, \mathcal{D},\, \mathcal{A},\, C,\, L,\, \mathcal{O},\, \Omega \rangle$$, where $\mathcal{P}$ is players/agents, $\mathcal{T}$ is substate tracks, $\mathcal{D}$ is decisions, $\mathcal{A}$ is actions, $C$ is the consequence function, $L$ is legality, $\mathcal{O}$ is outcomes, and $\Omega$ is outcome rules (Riggins et al., 2019).
• Perceived Game System (PGS): Delineates what information is revealed or concealed to participants, capturing aspects such as "fog of war" or partial observability.
• Game Representation and Actualization: Refers to the physical or digital instantiations, including user interfaces, visualization systems, or embodied simulations.
• Agents: Autonomous entities (human or machine) that enact strategies, ranging from rule-based execution (as in CAICL-coded Cybugs (Ahmed, 2010)) to creative, persona-driven narrative action (as with LLM-powered system agents (Hogan et al., 17 Apr 2024)).

A multi-dimensional framework further distinguishes wargames by the “creativity” of player and adjudicator roles, yielding quadrants that span from rule-constrained analytical games (e.g., Chess) to open-ended narrative simulations (e.g., seminar-style crisis wargames, D&D) (Matlin et al., 21 Sep 2025).

2. Mathematical and Game-Theoretic Foundations

Modern wargame ontology is underpinned by rigorous mathematical models that formalize strategic interaction, decision processes, and utility tradeoffs:

• Game-Theoretic Models: Cyber wargaming is frequently modeled as a contest with discrete strategy sets for attacker and defender ($s_a$, $s_d$). Utilities are expressed as:

$$U_a(s_a, s_d) = b \cdot \left(\prod_{\ell} P_\ell(s_a, s_d)\right) - C_a(s_a, s_d)$$

$U_d(s_a, s_d) = b \cdot (1 - P_T) - C_d(s_a, s_d)$

where $b$ is the benefit, $P_T$ is cumulative penetration probability, $C_a$/$C_d$ are costs (Colbert et al., 2018). Equilibria are analyzed via Nash, Stackelberg, or opponent-driven solution concepts.

• Multi-Attribute Decision Making (MADM): Complex environments require evaluation across heterogeneous attributes (distance, speed, capability). Attributes are normalized via intuitionistic fuzzy numbers:

$$\text{IFN:} \quad A = \{x; \mu_A(x),\, \nu_A(x) \mid x \in X;\ 0 \leq \mu + \nu \leq 1\}$$

Aggregation operators (e.g., IFWA) and entropy-based weighting methods compute comprehensive threat assessments (Sun et al., 2021).

• System Equivalences: Game tree equivalence up to relabeling and agency equivalence abstract away procedural and interface differences that do not affect true strategic agency (Riggins et al., 2019).

This formalism enables systematic comparison, automated reasoning, and strategic planning in simulated or real-world contexts.

3. Automation, AI, and LLMs

Advances in AI have transformed wargame execution, automation, and analysis across both quantitative (discrete, rule-driven) and qualitative (narrative, open-ended) domains:

• Deep Reinforcement Learning: Hierarchical and model-based RL, as in PPO and Actor-Critic (AC) frameworks, accelerate convergence and strategic adaptation in large, adversarial environments. Multi-attribute reward shaping through threat-based feedback significantly improves performance over pure RL, with reported win-rate increases (e.g., from 62% to 78% in MADM-PPO vs. PPO experiments) (Sun et al., 2021).
• Simulation Platforms: Software architectures (e.g., Snow Globe) implement multi-agent control, player, and team agents, leveraging LLMs for scenario generation, persona modeling, and adjudication. The modular approach supports zero-shot adaptability and rapid iteration, with dynamic history tracking $H = [h_1, \dots, h_n]$ encoding context across rounds (Hogan et al., 17 Apr 2024).
• LLMs in Qualitative Wargames: Automation of open-ended text-based wargames enables creative, context-rich gameplay and analysis. Adjudication processes instructions such as "Include unexpected consequences," reframing hallucination as a mechanism for plausible complexity, and high throughput simulation for policy exploration (Hogan et al., 17 Apr 2024, Matlin et al., 21 Sep 2025).
• Safety and Best Practices: Deployment of LMs in strategic contexts requires countermeasures for prompt sensitivity, escalatory bias, unfaithful reasoning, context incoherence, and implicit alignment. Hybrid human-AI oversight and robust evaluation protocols are recommended (Matlin et al., 21 Sep 2025).

These developments expand the ontology to encompass both analytical and creative dimensions of game structure and execution.

4. Application Domains and Case Studies

Wargames have found applications across military, cybersecurity, bioprocessing, crisis management, and entertainment domains, with each context presenting unique design and analytical challenges:

Domain	Example Scenario	Key Ontological Feature
Military	Tabletop COA generation	Game-theoretic matrices, equilibrium analysis (Colbert et al., 2018)
Cybersecurity	Penetration probability games	Layered defense modeling, payoff computation (Colbert et al., 2018, Reddie et al., 2023)
Biocybersecurity	Vulnerability assessment drills	Simulation of bio-cyber interactions, role-based exercises (Potter et al., 2020)
Policy Simulation	Crisis escalation games	Balancing realism, analytical utility, and engagement (Reddie et al., 2023)
AI Incident Resp.	LLM-powered tabletop exercises	Persona modeling, rapid iteration, outcome analysis (Hogan et al., 17 Apr 2024)
Entertainment	Narrative wargames (D&D)	Creative player/adjudicator axes (Matlin et al., 21 Sep 2025)

These case studies illustrate the broad applicability of the ontology and the necessity of adapting game design to specific research or operational objectives.

5. Methodological Tradeoffs and the Wargamer's Trilemma

Design and analysis of wargames entail navigating key tradeoffs, encapsulated by the "wargamer's trilemma": analytical utility, contextual realism, and engaging play (Reddie et al., 2023).

• Analytical Utility: Precision and control in isolating strategic variables for data collection and hypothesis testing.
• Contextual Realism: Fidelity in representing domain- or scenario-specific complexities, often required for external validity.
• Engaging Play: Emotional and cognitive involvement of participants, essential for authentic decision-making and emergent behavior.

Optimal design requires balancing these objectives, as excessive abstraction may omit critical nuance, and excess realism may introduce confounding variables or reduce engagement. Automated systems must account for these dimensions in scenario construction and outcome adjudication.

6. Open Challenges and Future Directions

The ontology of wargames continues to evolve in light of expanding automation, methodological innovation, and interdisciplinary integration. Open research challenges include:

• Evaluation Protocols: Development of metrics and benchmarks for long-horizon, LM-driven strategic reasoning and outcome accuracy (Matlin et al., 21 Sep 2025).
• Robustness: Ensuring LM and AI-driven agents maintain coherence under distributional shifts or novel scenarios.
• World Modeling: Integration of dynamic, adaptive models for predicting and simulating the strategic effects of open-ended moves over extended sessions.
• Persona Management: Ensuring faithful, interpretable persona modeling in multi-agent simulations, including transparent reasoning chains.
• Human-AI Interaction: Comparative paper of mixed vs. automated agent teams, and the design of interfaces for optimal collaboration and oversight.

This expanding research agenda is foundational to the continued refinement and application of wargame ontologies across domains.

7. Significance and Outlook

The ontology of wargames provides the formal and conceptual infrastructure for designing, analyzing, and automating complex decision-making simulations. Incorporating rigorous mathematical foundations, advanced AI methodologies, and structured creativity axes, this ontology supports a wide spectrum of applications—from military strategy evaluation and cyber defense to scenario-based policy exploration and creative entertainment. Ongoing work on methodological tradeoffs, evaluation, and robust automation promises to further systematize the field, expand the scope for interdisciplinary research, and enhance the capacity for real-world impact.