Below is a structured comparison of Clausewitzian friction, rational‑actor models, and complex adaptive systems (CAS) as conceptual foundations for AI‑assisted wargaming, with definitions, methodological implications, AI techniques, and trade‑offs.

Foundational concepts and implications for wargaming

Clausewitzian friction

• Definition and core implication: Clausewitzian friction is best understood as a condition—resisting forces and interactions—that disrupts plans and magnifies uncertainty as operations scale and become more complex; it is not a single “object” but a pervasive force that impedes realizing even the best‑laid designs in war Clausewitzian friction is not an object, but a condition. Friction is a Newtonian concept, which refers to the resistant force between two interacting surfaces^[2] Clausewitz acknowledges that friction creates enormous difficulties for the realization of any plan^[3]. This “condition” includes uncertainty about both adversary and self, and new technologies can paradoxically exacerbate friction by increasing uncertainty and chaos in human systems Paradoxically, however, new technologies that reduce the role of humans in fact may exacerbate friction by increasing uncertainty and the^[7] Our uncertainty about the situation at a given moment is not limited to the conditions of the enemy only but of our own army as well^[10].
• Clausewitz’s trinity reinforces that war is a system of interacting tendencies (people, commander and force, state), making plan execution a deeply coupled, socio‑technical problem; modeling must accommodate multiple adaptive perspectives rather than a single adversary algorithm Clausewitz describes war in holistic terms as a paradoxical trinity comprised of the tendencies of the people, the commander and his army, and the government^[8] Hybrid warfare is an operational concept where military and non-military capabilities are optimised to distort reason, shape passion, and leverage chance^[9]. This frames wargaming around emergent events, cognitive biases, and chance as equal players to the map and rules.
• Pragmatic wargaming reality: bounded rationality limits analysts and participants; formalizing all uncertainty is infeasible, so models must encode what humans can credibly reason about while leaving room for indeterminacy and qualitative judgments In techniques other than free-form gaming the bounded rationality of the analyst bounds the study^[5].

Rational‑actor (expected utility and game‑theoretic) models

• Core assumptions: actors are utility‑maximizing, fully informed, and consistent, choosing among well‑defined strategies/acts under known payoffs; sequences go from information acquisition to strategy space definition to choice The rational actor theory states that individuals are rational decision-makers who evaluate all of the information and options available to them to make^[11] The rational actor model treats foreign policy choices as products of the fol- lowing idealized sequence. Given some problem, a rational^[12]. Risk is handled by explicit probability distributions over outcomes and expected utility maximization Bounded Rationality - Stanford Encyclopedia of Philosophy^[14].
• AI alignment and strengths: AI can instantiate rational‑actor play by optimizing choices under known or learned payoff structures, solving for equilibria or policies, and running large‑scale decision‑support loops; recent systems explicitly use Bayesian networks and neural methods to capture perspectives and opponent calculations within wargames AI should help participants in wargames, and agents in simulations, to understand possible perspectives, perceptions, and calculations of adversaries who are^[23]. Risk‑aware, optimization‑forward decision pipelines (e.g., planning under partial observability) map naturally to rational‑actor abstractions We present Red Force Response (RFR), a decision support tool that exploits AI in a wargaming simulator to find potential Red Force CoAs. Using state-of-the-art^[33].
• Key critiques: Expected utility theory (EUT) assumes logical, well‑informed consistency; empirical and philosophical work shows many human decisions violate these assumptions under uncertainty, time pressure, or ambiguity, motivating bounded‑rational and robust/ambiguous models EUT presumes that individuals making judgments are reliable, logical, and well-informed. "Consistency" is the tendency for people to make decisions that match^[15] Bounded Rationality now describes a wide range of descriptive, normative, and prescriptive accounts of effective behavior which depart from the assumptions of^[14]. Security‑studies critiques similarly argue that EUT’s dominance may blind analysis to perception, identity, and institutional path dependencies in crises This article critically examines the prevailing definitions of rationality within security studies, particularly the dominance of expected utility theory^[20].

Complex adaptive systems (CAS) and agent‑based modeling

• Emergence and adaptation: CAS emphasize nonlinear interactions, decentralized adaptation, and emergent behavior where macro patterns can only be inferred from micro‑level rules; in security/wargaming, terrain, information dominance, and human organizations can produce emergent events that invalidate static payoff matrices Emergent behavior in complex systems engineering: a modeling and simulation approach^[24] Agent-Based Modelling and Geographical Information Systems^[23] Agent-based Modeling (ABM) and its resulting emergent behavior is a potential solution to model terrain in terms of the human domain and improve the results and^[22].
• AI’s role in CAS‑style wargaming: Machine learning (e.g., neural networks) complements Bayesian methods to recognize patterns, infer opponent strategies, and simulate emergent organizations; evolutionary and Bayesian game techniques approximate equilibria and strategic learning when type/action spaces are high‑dimensional Neural Network: Unlike Bayesian networks which rely on pre‑ defined relationships, neural networks, which are modeled on the human brain, learn^[35] Bayesian networks (BN) are a family of probabilistic graphical models representing a joint distribution for a set of random^[37] We address the problem of solving complex Bayesian games, characterized by high-dimensional type and action spaces^[36] Evolutionary Game Theory is an application of game theory to evolving populations of organisms. Of recent interest are EGT mod- els situated on structured ...^[31]. ABM shows how cooperation, control, and markets can emerge from local interactions, paralleling battlefield human organization under stress and information limits The models ask questions such as “how do markets and cooperative behavior among agents emerge?” Thus, agent-based modeling also can be seen as “generative” ...^[28].
• Why CAS for wargaming: when the system is distributed and adaptive (command‑and‑control, networks, hybrid/irregular environments), ABM with learning agents better captures indeterminacy and the effects of “friction” as emergent uncertainty from many interacting constraints and perceptions Recent progress in Game AI has demonstrated that given enough data from human gameplay, or experience gained via simulations, machines can^[32] Recent progress in Game AI has demonstrated that given enough data from human gameplay, or experience gained via simulations, machines can^[39].

How AI implements each foundation in wargaming

• Encoding friction and uncertainty (probabilistic/AI methods) • Probabilistic graphical models and neural nets to encode belief states, chance nodes for “friction events,” and opponent uncertainty; these capture how indeterminacy and perceptions degrade plan value over time Neural Network: Unlike Bayesian networks which rely on pre‑ defined relationships, neural networks, which are modeled on the human brain, learn^[35] We present Red Force Response (RFR), a decision support tool that exploits AI in a wargaming simulator to find potential Red Force CoAs. Using state-of-the-art Bayesian networks (BN) are a family of probabilistic graphical models representing a joint distribution for a set of random^[23]. • Optimization under uncertainty (e.g., MDP/POMDP‑style planners) align with the Clausewitzian view that plans must anticipate disruptions; bounded‑rational heuristics and satisficing are justified when information is incomplete Bounded Rationality now describes a wide range of descriptive, normative, and prescriptive accounts of effective behavior which depart from the assumptions of^[14] In techniques other than free-form gaming the bounded rationality of the analyst bounds the study^[5].
• Rational‑actor play (optimization/game‑theory) • AI constructs strategy spaces, evaluates expected utilities/payoffs, and selects optimal or equilibrium strategies; Bayesian‑game solvers and learning‑from‑simulations populate best responses and meta‑reason about opponent beliefs AI should help participants in wargames, and agents in simulations, to understand possible perspectives, perceptions, and calculations of adversaries who are^[23] We address the problem of solving complex Bayesian games, characterized by high-dimensional type and action spaces^[36]. • Red‑team decision‑support systems search opponent courses of action (COAs) under uncertainty using state‑of‑the‑art representation learning and planning, operationalizing a rational‑actor loop at scale We present Red Force Response (RFR), a decision support tool that exploits AI in a wargaming simulator to find potential Red Force CoAs. Using state-of-the-art^[33].
• CAS/ABM (emergence, adaptation, hybrid human‑agent loops) • ABM and evolutionary learning to emulate adaptive forces, cities/infrastructure, and information environments; neural nets recognize battlefield patterns and emergent organization, while Bayesian networks relate variables and causal beliefs under limited understanding Neural network artificial intelligence may be needed to assist the understanding of emergent behaviors for architectural model development. Agent-based modeling ...^[26] Agent-based Modeling (ABM) and its resulting emergent behavior is a potential solution to model terrain in terms of the human domain and improve the results and^[27] Agent-based modelling the emergent behaviour of a system-of-systems^[38]. • Generative ABMs ask how cooperation and structures emerge from local interaction—informative for command, logistics, and information operations that hinge on human organization under stress and incomplete information The models ask questions such as “how do markets and cooperative behavior among agents emerge?” Thus, agent-based modeling also can be seen as “generative” ...^[28]. • Large‑scale “AI‑embedded” wargames simulate opponents/environments thousands to millions of times to surface conditions that reliably tilt outcomes—a CAS mindset where emergent properties are discovered through repeated, adaptive interaction Through AI-generated battlefield simulations, the Navy can fight an adversary force more than a million times to find a key to winning the battle^[25].

Trade‑offs and when to favor each foundation

• Fidelity vs. tractability under friction • Friction‑centric wargames need explicit chance and interaction terms to show how plans devolve into chaos; probabilistic/AI methods scale but may require assumptions on distributions, opponent priors, or latent variables that friction‑rich domains resist supplying Clausewitzian friction is not an object, but a condition. Friction is a Newtonian concept, which refers to the resistant force between two interacting surfaces^[2] Neural Network: Unlike Bayesian networks which rely on pre‑ defined relationships, neural networks, which are modeled on the human brain, learn^[35] Paradoxically, however, new technologies that reduce the role of humans in fact may exacerbate friction by increasing uncertainty and the^[7]. Decision‑support tools that exploit AI can mitigate planning blind spots but should be paired with human oversight to handle perception and passion beyond formal models We present Red Force Response (RFR), a decision support tool that exploits AI in a wargaming simulator to find potential Red Force CoAs. Using state-of-the-art^[33].
• Predictive clarity vs. bounded rationality constraints • Rational‑actor models deliver clear, traceable reasoning from data and models to COAs and risk analytics, enabling “what‑if” optimization under known or estimable distributions and payoffs; however, real‑time human factors (cognitive biases, ambiguity aversion, institutional paths) often violate EUT, calling for hybrid bounded‑rational solvers and qualitative “friction” layers The rational actor model treats foreign policy choices as products of the fol- lowing idealized sequence. Given some problem, a rational^[12] Bounded Rationality now describes a wide range of descriptive, normative, and prescriptive accounts of effective behavior which depart from the assumptions of^[14] This article critically examines the prevailing definitions of rationality within security studies, particularly the dominance of expected utility theory^[20].
• Emergent behavior vs. compute and specification burden • CAS/ABM captures the Clausewitzian “trinity” and hybrid dynamics by letting human and machine agents adapt locally; emergent properties discovered via simulation are rich but hard to certify, diagnose, or compress, and require careful validation to separate noise from system properties Clausewitz describes war in holistic terms as a paradoxical trinity comprised of the tendencies of the people, the commander and his army, and the government^[8] Agent-based Modeling (ABM) and its resulting emergent behavior is a potential solution to model terrain in terms of the human domain and improve the results and^[22] Emergent behavior in complex systems engineering: a modeling and simulation approach^[24]. Evolutionary and neural methods help, but scale and explainability remain challenges; research explicitly frames ABM with AI as a means to understand emergent behaviors across system‑of‑systems battlefields Neural Network: Unlike Bayesian networks which rely on pre‑ defined relationships, neural networks, which are modeled on the human brain, learn^[35] Evolutionary Game Theory is an application of game theory to evolving populations of organisms. Of recent interest are EGT mod- els situated on structured ...^[31].
• Hybridization trends in AI‑assisted wargaming • Contemporary efforts combine probabilistic modeling (Bayesian networks), neural pattern recognition, and optimization/game‑theory decision support—plus ABM/evolutionary learning—to capture uncertainty (friction), rational optimization where feasible, and adaptive learning where human/organizational behavior resists specification. These hybrids are reflected in AI‑embedded wargaming loops that run at high scale to “stress‑test” COAs under emergent conditions, and in red‑team DSS that integrate representation learning and planning to search adversary space Through AI-generated battlefield simulations, the Navy can fight an adversary force more than a million times to find a key to winning the battle^[25] We present Red Force Response (RFR), a decision support tool that exploits AI in a wargaming simulator to find potential Red Force CoAs. Using state-of-the-art^[33] Neural Network: Unlike Bayesian networks which rely on pre‑ defined relationships, neural networks, which are modeled on the human brain, learn^[35] Agent-based modelling the emergent behaviour of a system-of-systems^[38] AI should help participants in wargames, and agents in simulations, to understand possible perspectives, perceptions, and calculations of adversaries who are^[23]. • Critiques of pure EUT and platform‑agnostic guidance argue that AI should broaden, not replace, human judgment: tools ought to model perspectives, perceptions, and calculations, aligning with Clausewitzian trinity and hybrid wargaming realities rather than assuming perfectly rational actors AI should help participants in wargames, and agents in simulations, to understand possible perspectives, perceptions, and calculations of adversaries who are^[23] This article critically examines the prevailing definitions of rationality within security studies, particularly the dominance of expected utility theory^[20].

Practical guidance: choosing (and blending) foundations

• Favor Clausewitzian/fidelity‑first when the war problem is dominated by uncertainty, human cognition under stress, and chance; implement probabilistic/chance models, Bayesian networks/neural belief updates, and bounded‑rational heuristics, supported by analyst oversight; expect richer emergent events and plan brittleness under friction Clausewitz acknowledges that friction creates enormous difficulties for the realization of any plan^[3] Our uncertainty about the situation at a given moment is not limited to the conditions of the enemy only but of our own army as well^[10] Agent-based Modeling (ABM) and its resulting emergent behavior is a potential solution to model terrain in terms of the human domain and improve the results and^[27].
• Favor rational‑actor foundations when payoffs and strategies are measurable, and AI can optimize or reason to equilibria across transparent decision spaces; pair with Bayesian‑game solvers and large‑scale planning, but include robust/ambiguity‑aware methods to handle deep uncertainty and bounded information The rational actor model treats foreign policy choices as products of the fol- lowing idealized sequence. Given some problem, a rational^[12] We address the problem of solving complex Bayesian games, characterized by high-dimensional type and action spaces^[36] EUT presumes that individuals making judgments are reliable, logical, and well-informed. "Consistency" is the tendency for people to make decisions that match^[15].
• Favor CAS/ABM when adaptive human organizations, networks, and hybrid dynamics drive outcomes; equip agents with evolutionary learning and neural pattern recognition to capture emergent behavior, and use Bayesian belief networks to tie variables to strategic questions; validate emergent properties under controlled variance and explainability constraints Evolutionary Game Theory is an application of game theory to evolving populations of organisms. Of recent interest are EGT mod- els situated on structured ...^[31] Bayesian networks (BN) are a family of probabilistic graphical models representing a joint distribution for a set of random^[23] Emergent behavior in complex systems engineering: a modeling and simulation approach^[24].
• Build hybrids: combine chance nodes and belief updating for friction, optimization/game‑theory planners for executable COAs, and ABM/evolutionary learning for adaptive opponents and organizations; scale with AI‑embedded wargames and decision support; maintain a Clausewitzian lens by reserving space for chance, passion, and perception alongside formal calculations Through AI-generated battlefield simulations, the Navy can fight an adversary force more than a million times to find a key to winning the battle^[25] We present Red Force Response (RFR), a decision support tool that exploits AI in a wargaming simulator to find potential Red Force CoAs. Using state-of-the-art^[33] AI should help participants in wargames, and agents in simulations, to understand possible perspectives, perceptions, and calculations of adversaries who are^[23] Hybrid warfare is an operational concept where military and non-military capabilities are optimised to distort reason, shape passion, and leverage chance^[9].

Summary comparison at a glance

• Clausewitzian friction: decision‑centered uncertainty and indeterminacy; model as chance and interaction; use Bayesian neural belief systems, bounded‑rational heuristics, and human oversight; strengths in fidelity to real operations; limits in tractability and specification bias Clausewitz acknowledges that friction creates enormous difficulties for the realization of any plan^[3] Neural Network: Unlike Bayesian networks which rely on pre‑ defined relationships, neural networks, which are modeled on the human brain, learn^[35] Bounded Rationality now describes a wide range of descriptive, normative, and prescriptive accounts of effective behavior which depart from the assumptions of^[14].
• Rational actor models: payoff‑ and choice‑centric; AI brings optimization and equilibrium computation; best when data/measurement support EUT; complemented by robust/ambiguous models; strengths in predictability and auditability; limits when human bias and ambiguity dominate The rational actor model treats foreign policy choices as products of the fol- lowing idealized sequence. Given some problem, a rational^[12] We address the problem of solving complex Bayesian games, characterized by high-dimensional type and action spaces^[36] EUT presumes that individuals making judgments are reliable, logical, and well-informed. "Consistency" is the tendency for people to make decisions that match^[15].
• Complex adaptive systems: organization/interaction‑centric; AI enables ABM, evolutionary learning, and neural pattern discovery; strengths in emergent behavior and hybrid environments; limits in explainability and verification; best paired with probabilistic overlays and human judgment Emergent behavior in complex systems engineering: a modeling and simulation approach^[24] Evolutionary Game Theory is an application of game theory to evolving populations of organisms. Of recent interest are EGT mod- els situated on structured ...^[31] Neural Network: Unlike Bayesian networks which rely on pre‑ defined relationships, neural networks, which are modeled on the human brain, learn^[35].

In short, AI‑assisted wargaming grounded in Clausewitzian friction emphasizes uncertainty and bounded rationale with probabilistic/AI belief and decision support; rational‑actor foundations deliver optimization and equilibrium reasoning under measurable risk but require robustification to human fallibility; CAS/ABM capture adaptive, emergent command–terrain–information dynamics with learning agents and neural pattern models; cutting‑edge systems blend these pillars to reflect the Clausewitzian “trinity” and the hybrid realities of modern conflict Clausewitz describes war in holistic terms as a paradoxical trinity comprised of the tendencies of the people, the commander and his army, and the government^[8] Agent-based Modeling (ABM) and its resulting emergent behavior is a potential solution to model terrain in terms of the human domain and improve the results and^[22] AI should help participants in wargames, and agents in simulations, to understand possible perspectives, perceptions, and calculations of adversaries who are^[23].