# Symbiotic Game and Foundation Models for Cyber Deception Operations in
Strategic Cyber Warfare

Tao Li and Quanyan Zhu

###### Abstract

We are currently facing unprecedented cyber warfare with the rapid evolution
of tactics, increasing asymmetry of intelligence, and the growing
accessibility of hacking tools. In this landscape, cyber deception emerges as
a critical component of our defense strategy against increasingly
sophisticated attacks. This chapter aims to highlight the pivotal role of
game-theoretic models and foundation models (FMs) in analyzing, designing, and
implementing cyber deception tactics. Game models (GMs) serve as a
foundational framework for modeling diverse adversarial interactions, allowing
us to encapsulate both adversarial knowledge and domain-specific insights.
Meanwhile, FMs serve as the building blocks for creating tailored machine
learning models suited to given applications. By leveraging the synergy
between GMs and FMs, we can advance proactive and automated cyber defense
mechanisms by not only securing our networks against attacks but also
enhancing their resilience against well-planned operations. This chapter
discusses the games at the tactical, operational, and strategic levels of
warfare, delves into the symbiotic relationship between these methodologies,
and explores relevant applications where such a framework can make a
substantial impact in cybersecurity. The chapter discusses the promising
direction of the multi-agent neurosymbolic conjectural learning (MANSCOL),
which allows the defender to predict adversarial behaviors, design adaptive
defensive deception tactics, and synthesize knowledge for the operational
level synthesis and adaptation. FMs serve as pivotal tools across various
functions for MANSCOL, including reinforcement learning, knowledge
assimilation, formation of conjectures, and contextual representation. This
chapter concludes with the discussion of the challenges associated with the
FMs and their application in the domain of cybersecurity.

##  1 Introduction

Addressing network security challenges is increasingly daunting due to the
rise of highly sophisticated attackers, often backed by significant funding
and resources from nation-states. These adversaries possess ample resources,
including advanced capabilities, dedicated personnel, and deep knowledge,
enabling them to pursue their objectives with precision. Traditional defense
mechanisms, such as encryption and firewalls, are no longer sufficient in this
evolving landscape. In fact, contemporary network security issues have evolved
into a form of cyber warfare, wherein adversaries leverage digital
technologies to target assets for strategic, political, or military gains. The
cyber warfare can be integrated into physical domains. Adversaries can exploit
vulnerabilities in both cyber and physical infrastructure in a coordinated
fashion to gain a strategic advantage over their opponents.

Through offensive operations, employing tactics like the cyber kill chain,
adversaries deploy multiple attack vectors to undermine critical systems in a
stealthy and persistent manner. In response, defenders are tasked with
safeguarding their assets against cyber threats and attacks. The essence of
cyber defense lies in outmaneuvering the attacker through innovative
strategies and technologies to thwart malicious activities and preserve the
integrity of network infrastructure. To this end, recent trends have focused
on automated, proactive, and adaptive defenses that are able to reduce
cognitive demands, improve operational tempo and mission speeds, gain
information advantage, and achieve decision dominance.

Cyber deception emerges as one promising class of defenses, involving the
creation of traps, decoys, or false information to mislead attackers and
divert their attention from valuable assets or genuine security measures [51,
1]. The deployment of cyber deception techniques enables network systems to
detect, delay, or disrupt attackers’ activities while gathering intelligence
about their tactics, techniques, and procedures (TTPs). An automated and
adaptive cyber deception strategy can proactively predict and respond to
attackers’ behaviors by creating further deception to deter the attack or
engage attackers to gather information. By minimizing the involvement of human
operators in the cyber response workflow and intelligently aligning tactical
responses with mission objectives, this approach facilitates faster and more
mission-aligned decision-making, enhancing cyber resilience for the mission.

###  1.1 Role of Game-Theoretic Models

The interaction between defenders and attackers in cyber deception and the
cyber warfare in general is often conceptualized as a strategic game, wherein
both parties endeavor to outmaneuver the other to achieve their respective
goals. In recent literature, many game models (GMs) serve a descriptive
framework, wherein a specific attack model, including strategies, objectives,
and information structures, is assumed alongside a defender model [63].
Subsequently, the analysis of the game aims to find the equilibria of the
game, which include equilibrium payoffs, strategies, and, in dynamic games,
equilibrium dynamics or trajectories.

The overarching aim of this analytical endeavor is twofold. Firstly, it seeks
to forecast the long-term outcomes of cyber warfare by evaluating the
defender’s optimal response to repeated attacks orchestrated by adversaries.
Secondly, it endeavors to use equilibrium policies as robust defense
mechanisms. These strategies are suitable to serve as default approaches in
situations where no real-time information about the attackers is accessible,
and hence, there is a need for assumptions about worst-case scenarios to
ensure performance-guaranteed strategies. However, in scenarios where
information is available, albeit incomplete, through intelligence gathering
and online observation, a dynamic adaptation of strategies can be implemented
to complement these default policies, thereby enhancing the resilience of
defensive measures.

This methodological framework finds applications across diverse domains,
including jamming games [104, 106, 91, 71], authentication games [30, 82, 29,
34, 84], routing games [101, 109, 21], intrusion detection [80, 40, 100, 107],
infrastructure protection games [16, 42, 12, 11, 41], and insider threat [47,
8, 9, 25, 65]. These endeavors yield valuable insights and establish a
fundamental understanding of adversarial interactions at a higher level.
Typically, the equilibrium analysis of these models plays a crucial role in
informing strategic-level decisions, such as risk assessment, investment
decisions, and resource planning within organizations and security contexts.
Several factors contribute to the significance of equilibrium. Firstly, the
credibility of equilibrium forecasts increases as games are played repeatedly
over an extended period. With time, players tend to figure out the structure
and the rule of the game, adopt rational strategies, and make more informed
decision-making. Secondly, strategic-level decisions do not mandate a high-
level precision of the details of implementation and operations and thus can
rely on the equilibrium prediction. A rough estimate of the equilibrium
outcomes within the correct magnitude suffices for effective high-level
decision-making processes. One area for which game-theoretic frameworks have
offered valuable tools is the strategic risk analysis against a variety of
adversarial models, each representing contingent goal-driven adversaries [81,
19, 14]. This application is particularly vital within cybersecurity contexts,
where predicting adversarial behaviors proves challenging, unlike natural
events governed by probabilistic distributions. Adversarial TTPs drive these
behaviors. Leveraging game theory provides a distinctive framework for cyber
risk analysis, with implications spanning domains like cyber insurance [95,
93, 85, 94], cyber-physical system integration [46, 18, 108, 46], and security
investment [10, 33, 15, 17].

Figure 1: Multi-level game-theoretic frameworks: strategic level, operational
level, and tactical level games. Strategic level games are games that describe
high-level decision-making, such as resource allocations and investment
planning. The goal of strategic level games is to create long-term planning to
achieve overarching objectives of the cyber warefare. Tactical-level games
involve specific actions and maneuvers that can be implemented to achieve
immediate objectives to support the overarching strategy. Examples of tactics
in cyber warfare include the configuration of honeypots and the attacker
engagement policies. The operational-level games sit between the strategic and
tactical levels, focusing on the planning and coordination of a sequence of
defense actions. Examples include the planning of a series of cyber defense
strategies starting from intelligence gathering to counter lateral movement to
achieve strategic level goals. Figure 2: An example of game modeling: An
attacker aims to carry out a cyber kill chain to reach the target while a
defender aims to deter and thwart this operation. The goal of the attacker is
determined through strategic-level reasoning. It can be viewed as an outcome
of a high-level game description. Once the goal is set, the cyber kill chain
determines the tactics, techniques, and procedures (TTP) to achieve its goal,
while the defender determines the defending TTPs. This operation is composed
of a sequence of tactic-level games can provide specific techniques and
actions. Each tactic level game corresponds to a stage in the operation. The
games will yield tactics that determine the outcome at each stage and,
eventually, the outcome of the operation. An adaptive operation is often used
to reconfigure the operation when the operation fails at certain stages. In
this case, the games will need to be redesigned and synthesized to adapt to
the uncertainties in the outcomes.

However, the lack of precision makes it less applicable to tactical scenarios
where details of how to act are imperative in the face of an attack. Obtaining
exact models of the game proves challenging, particularly regarding the
strategies of attackers and their knowledge. Sometimes, it is also challenging
for the defender itself to figure out the knowledge and available strategies.
To address this challenge, literature often turns to more intricate modeling
approaches, such as Bayesian games [36, 37] and hypergames [4, 88], to
accommodate uncertainties. In particular, in the domain of cyber deception,
where information asymmetry is prevalent, Bayesian games have emerged as an
appropriate class for describing cyber deception scenarios. These scenarios
involve various tactics such as honeypot configuration [54, 55, 5], attack
engagement [45, 46, 7], and information design [98, 97, 96], among others.

While the Bayesian approach provides new insights into games of incomplete
information by formally modeling imperfect observations and uncertainties
about game variables, it shifts the challenges toward uncertainty
quantification of underlying unknowns, introducing new complexities to the
modeling process. As uncertainties multiply, especially when dealing with
numerous uncertain parameters or structures, the model’s complexity escalates.
For instance, when uncertain parameters are continuous variables, quantifying
uncertainty in random variables becomes a formidable task.

Uncertainty quantification often requires a substantial amount of data or
repeated interactions between attackers and defenders within the same
environment to establish reliable distributions. However, obtaining such data
poses challenges, as the game is not time-invariant, and the rounds of
interactions between attackers and defenders are limited, which further
constrains the observables obtained from these interactions.

Moreover, while this approach is reasonable for handling structured
uncertainties (i.e., known unknowns), it encounters difficulties with
unstructured uncertainties (e.g., epistemic uncertainties). Furthermore, even
with a well-defined model, computing equilibrium concepts like Bayesian
equilibrium proves challenging [64] and often lacks predictive power,
especially in dynamic tactical environments characterized by nonstationary
behaviors and conditions.

It is imperative to go beyond the current approach. Recently, nonstationary
reinforcement learning and nonequilibrium solutions have emerged as prominent
ways to tackle this challenge. Nonstationary reinforcement learning aims to
tackle the nonstationary nature inherent in learning environments. In security
games, an agent’s game can undergo changes due to the dynamics of the
knowledge and behaviors of other players. Additionally, the joint actions
taken by the players of the game can lead to shifts in the game environment.
It is one type of internalized nonstationarity, which is caused by the players
themselves. Externalized nonstationarity refers to changes caused by exogenous
factors; for instance, in cyber warfare, the disclosure of vulnerabilities to
the public can alter the game dynamics between defenders and attackers due to
the change in the information structure.

Learning in a nonstationary environment poses challenges as strategies adapted
to earlier games must be re-evaluated for new environments [63]. Unlike in
stationary environments, where learning strategies often converge to relevant
equilibrium concepts [62], nonstationary games cannot be characterized by
equilibrium, and there is a need for a reevaluation of reinforcement learning
goals. Learning strategies do not need to aim to converge to an equilibrium
outcome [66]; rather, an equilibrium outcome can be viewed as a result of
learning behaviors [75]. This perspective can lead to the nonequilibrium
solutions that redefine outcomes for nonstationary games [35]. Nonequilibrium
solutions are relevant even in stationary games where interactions are
limited, meaning players cannot reach equilibrium within short timeframes.

###  1.2 Role of Foundation Models

Such approaches offer promising avenues to navigate the complexities of
dynamic tactical environments where traditional equilibrium concepts may prove
insufficient. The advent of foundation models (FMs) introduces a new dimension
of possibility to this endeavor. These models enable the encoding of game
descriptions through more sophisticated frameworks, offering enhanced
precision in capturing detailed aspects of the game. For instance, FMs can
encapsulate the knowledge structure of attackers, non-Markov dynamics (e.g.,
time series data), and diverse attacker types. This granularity holds the
potential to provide tactical-level solutions, thereby facilitating improved
decision-making processes.

Moreover, FMs facilitate the modeling of flexible learning and reasoning
processes of varying styles. Unlike current approaches that are often pre-
specified in terms of learning methods and objectives, this adaptability
allows for the creation of novel solution concepts capable of describing
outcomes within limited interactions, nonstationary environments, and non-
Markovian behaviors. Such models are particularly suitable for generating
practical, real-time tactics that can achieve decision dominance.

Furthermore, FMs enable not only descriptive modeling but also prescriptive
and predictive features. Prescriptive analytics directly yield end-to-end
intelligence that informs tactics, bypassing the separate process of modeling
the entire game, defining and finding the associated solutions, and creating
decision-dominant tactics. This end-to-end approach facilitates the
translation of information directly into actionable and adaptive tactics.

Another pivotal aspect of FMs lies in their predictive analytics capability,
which plays an important role in warfare scenarios. The ability to anticipate
and promptly respond to emerging threats can be a decisive factor. Predictive
analytics serves several critical functions in tactical reasoning. Firstly, it
enables defenders to forecast the dynamic environment, including the
anticipated behaviors of adversaries and the external factors influencing
environmental shifts. This foresight enables proactive measures to mitigate
risks. Secondly, predictive analytics integrates into the learning and
adaptation of strategies, enabling the formulation of look-ahead strategies.
These strategies analyze subsequent subgames and anticipate potential counter-
strategies from attackers, thereby creating decision-dominant tactics in
cyberwarfare. The incorporation of predictive analytics into FMs enhances
their adaptability and effectiveness in navigating dynamic and adversarial
environments.

###  1.3 Cyber Deception and Related Game-Theoretic and Foundation Models

Cyber deception is an overt operation. Defenders need to design mechanisms to
outsmart attackers, leading them to fall into honeypots or unwittingly
disclose information beneficial to the defender’s objectives. The application
of FMs to cyber deception games is an ideal synergy. FMs can contribute to
this goal by improving analytical capabilities crucial for strategic
reasoning. A significant challenge in cyber deception lies in the inherent
uncertainties. The environment is rife with unknowns, including imprecise
knowledge of attacker attributes. It remains unclear whether attackers are
aware of the deception and may deploy counterdeception tactics. Additionally,
the behaviors of non-attackers, such as normal users, pose another layer of
uncertainty. While deceiving normal users is not the intent of cyber
deception, their errors can inadvertently diminish its efficacy. FMs offer
invaluable tools for addressing these challenges, facilitating hierarchical
and predictive reasoning to enhance decision-making processes. For instance,
models can anticipate attacker responses to deception and utilize cognitive
hierarchies to optimize decisions. Predictive reasoning enables the
anticipation of both attacker actions and user behaviors in subsequent steps,
thereby preparing defenders to preempt attacks and mitigate user errors
effectively.

The essence of cyber deception resonates strongly with game-theoretic models.
Cyber deception has essential characteristics that align closely with game-
theoretic attributes, including the information asymmetry between the players,
multi-stage and multi-phase interactions, the presence of aleatoric and
epistemic uncertainties, together with the bounded rational human behaviors.
In [77], a taxonomy of cyber deception games is developed to connect each
deception scenario with a fundamental class of game-theoretic models. The
taxonomy leads to a library of game building blocks that can be used to
synthesize multi-round multi-scale dynamic games that capture the cyber kill
and defense chains for strategic, operational, and tactic level decision-
making. For example, honeypot engagement has been captured by a class of
stochastic games with one-sided information. Honeypot deployment problems have
been captured by network design games. Intrusion evasion games have been
captured by a class of principal-agent detection games. These building blocks
enable a divide-and-conquer and modular approach to design cyber defense.
These modular games can be fused together with FMs to create function modules
that are capable of representing games in the security scenario to provide
strengthened learning and computation power. This enables the development of
tactical-level applications and the enhancement of cyber deception techniques.

With the aid of game theoretic frameworks, which capture the intricate
dynamics of cyber deception, the informed use of FMs becomes possible. Game-
theoretic frameworks facilitate the training and adaptation of FMs to suit
contextual applications with symbolic representation of the attacker-defender
interactions. Integrating game-theoretic models with FMs can play useful roles
across different phases of the cyber deception process. During the initial
design phase, FMs serve as invaluable tools for training and preparation.
Subsequently, they enable reinforcement learning, enabling adaptability and
refinement as the cyber deception strategy evolves. In the post-implementation
phase, FMs support adaptive tuning, ensuring ongoing optimization and
effectiveness of cyber deception techniques.

There are several ways to integrate the both. One approach is neurosymbolic
learning, where hybrid AI algorithms combine symbolic reasoning with data-
driven learning, resulting in robust and trustworthy systems. Symbolic
reasoning using game-theoretic models offers the capacity to incorporate
sophisticated abstractions grounded in system and game theories and associated
formalisms. Supported by advanced tools and methods, neurosymbolic learning
enables integrated analysis and assurance, leveraging formal specification and
verification technologies. These capabilities can be instrumental in
strengthening cyber deception mechanisms. Likewise, meta-reinforcement
learning represents another avenue for integrating FMs with game theory. This
approach involves developing models capable of learning from a diverse array
of game-theoretic security contexts rather than being restricted to a singular
context. Meta-reinforcement learning builds on the trained models to create
adaptive and self-improving cyber deception systems.

Meta-reinforcement learning and neurosymbolic learning can be integrated to
form an iterative process where game-theoretic domain knowledge evolves based
on observations, while defense policies adapt using reinforcement learning
methodologies. This process intertwines data-driven updates with domain-
specific game-theoretic primitives to result in a hybrid neural and symbolic
representation. This process can be empowered by FMs, and it will converge
towards an optimal combined hybrid neural and symbolic representation.

Large language models (LLMs) stand out as pivotal FMs well known for their
proficiency in handling textual and heterogeneous data. Their unparalleled
capacity to comprehend extensive textual datasets makes them indispensable for
natural language processing tasks, enabling the processing of text, time-
series data, and predictive analytics. In cybersecurity, they empower the
augmentation of network security through human-like language comprehension and
predictive capabilities. Within the domain of cyber deception, LLMs can
generate honey files such as counterfeit documents and credentials to entice
potential attackers. Moreover, LLMs excel in processing heterogeneous datasets
encompassing network traffic, system logs, and user behaviors to detect
anomalies, infer potential attacker behaviors, and predict malicious
activities. When encountering evolving threats, LLMs adeptly can automate
cyber deception policies to mitigate risks by putting together multiple
sources of information, including new vulnerability disclosure, defender’s
service requirements, and the current system state.

This chapter aims to introduce the symbiotic relationship between game-
theoretic models and FMs, focusing on their implications in cybersecurity and
cyber deception domains. Figure 3 illustrates this relationship. FMs serve as
the building blocks for AI applications and research, providing developers and
researchers with a solid platform to pioneer and innovate in artificial
intelligence and machine learning. Security games stand as building blocks in
cybersecurity applications, offering contextual and reasoned frameworks that
encapsulate the interactions between attackers and defenders across diverse
scenarios. The synergy of these models promises a transformative approach to
designing guardware that provides autonomous and proactive security measures.
In particular, the integration lays the groundwork for designing cyber
deception mechanisms that were used to be regarded as cumbersome, limited, or
challenging. By leveraging these foundational designs, we can forge a new
paradigm of intelligent security mechanisms and win cyber warfare.

Figure 3: Game-theoretic models and FMs are fused together to create function
modules for cyber defense, which will be built into the guardware. Game-
theoretic models are representations of security scenarios while FMs are
tailored for different tasks and applications. The guardware is composed of
multiple function modules that are enabled different games and FMs. Each
function module requires a different architecture to synthesize game and FMs.

###  1.4 Organization of the Chapter

This chapter is organized as follows. Section 2 provides the background on
cyber deception and network security games. It discusses the game-theoretic
approach to cyber adversarial modeling and the associated analytical, design,
and learning approaches. Section 3 provides a background on FMs and their
roles in AI, learning, and their relevance in cybersecurity. Section 4
presents the synergy of game-theoretic models and FMs in the context of cyber
deception. Section 5 presents several challenges and future directions that
need to be addressed to develop transformative security technologies. Chapter
6 concludes this chapter.

##  2 Cyber Deception and Network Security Games

Security games capture the intricate interactions between attackers and
defenders in various contexts. These scenarios span from cybersecurity
applications, involving the interaction between intruders and network system
administrators, to critical national security applications where safeguarding
pivotal assets, such as airports and infrastructures, is paramount against
potential terrorist threats. The formalization of security games frequently
relies on game-theoretic languages, specifying essential elements like
payoffs, players, and action sets.

Cyber deception stands out due to its unique tactics and objectives, which
involve the strategic deployment of decoys, honeypots, and false information
to manipulate attackers’ perceptions of the network and influence their
actions. The primary aim of deception is twofold: to deter attacks from
exploiting unknown vulnerabilities within our systems and to gain valuable
intelligence from attackers’ behaviors. Game-theoretic models for cyber
deception often revolve around information structures. For instance,
asymmetric information games elucidate the information asymmetry between two
players. Signaling games serve as a fundamental framework for understanding
two-player deception scenarios, where one player observes the true state of
the world while the other player can only observe messages or actions. They
have been applied to study detection evasion [40], honeypots [76], and insider
threats [8].

Stochastic games with one-sided information, e.g., in [39, 58, 2], extend this
framework into dynamic settings, where one player has complete observation of
the state space while the other player navigates with incomplete information,
forming beliefs over the state space. Information acquisition games facilitate
the trade-off between the cost of gathering information and the quality of
decision-making based on such information. Recent literature has been
investigating the design of observation kernels [67, 99] and optimal timing
for information acquisition [49, 50, 48].

###  2.1 Multi-Level and Multi-Scale Game Models

Decision-making in cybersecurity is multi-scale. We define three levels of
modeling, which require distinct levels of granularity. They are, namely,
strategic level, operational level, and tactic level. Cybersecurity problems
are growing nowadays into a cyber warfare. An attacker plans a kill chain that
involves multiple stages of attacks to achieve his planned goals. At the same
time, a defender aims to deter and thwart the operation of the attacker to
protect the target. The strategic level involves long-term planning and
decision-making aimed at achieving overarching goals and objectives. The
strategies are concerned with defining the overall goals, allocating
resources, and determining the target to attack or protect. The tactical level
involves specific actions and maneuvers implemented to achieve immediate
objectives and support the overarching strategy. The tactics include the
techniques, procedures, and actions that can be taken or implemented to carry
out a specific task. Examples include the tactics to engage an attacker in a
honeypot and the attacker’s tactics to do lateral movement to get to the
target. The operational level sits between the strategic and tactical levels,
focusing on the planning and coordination of multi-stage tactics to achieve
the specified mission from the strategic level. The operation involves
planning and replanning the multiple steps of tactics to achieve the goal of
compromising a targeted machine.

As illustrated in Fig. 1, the GMs involved at the three levels are multi-
scale. At the strategic level, the game is a high-level, coarse-grain
description of the adversarial interactions between a defender and an
attacker. For example, Blotto-type games, e.g., [83, 38, 31] have been
classically used to allocate a limited amount of resources to overpower
adversaries in cyber warfare by outnumbering their resources. FlipIt games and
their variants have also been recently studied in [86, 56, 6] to strategically
analyze the interplay between attackers and defenders, both striving to assert
control over a resource for the maximum duration while minimizing overall move
costs. Through strategic reasoning, defenders devise counterstrategies aimed
at controlling resources at opportune moments and minimizing downtime and
potential compromise. Network games are another class of strategic-level
security games. Networks are used to capture the interdependencies and
connectivity among the resources. The goal of the defender is to protect or
defend essential network assets and minimize the impact of the attacks. For
example, the framework proposed by [13] introduces a network design paradigm
allowing network designers to fortify links to establish redundant
communication pathways between nodes to mitigate potential attacks through
resource investment. By proactively considering strategic cyber threats, the
framework offers methods to characterize and compute optimal strategies for
securing a network within predefined budget constraints. In addition to
protective measures, resilient strategies for network recovery following
attacks are also essential in network defense. A two-player, three-stage game
framework proposed in [11] has aimed to capture both protection and recovery
phases. The network designer’s objective is to maintain network connectivity
both before and after an attack, while the adversary seeks to disrupt the
network by compromising specific links. This strategic game framework
facilitates analysis of trade-offs not only among nodes and links within the
network but also among resources allocated for pre-event protection and post-
event recovery.

The game at the operational level decomposes the objective of attacking and
defending a selected asset into multiple stages of operations. In accordance
with the cyber kill chain, attackers typically execute reconnaissance stages
before planning attacks, which involve footprinting, social engineering, and
intelligence gathering. Subsequently, after planning, the attack mission is
executed through the exploitation of vulnerabilities, privilege escalation,
and lateral movement to reach the targeted asset. For this operational
sequence, the reconnaissance stage can be modeled as a series of games that
delineate the process of information gathering through passive or proactive
means. The attacker’s planning following reconnaissance can also be modeled
through a sequence of games, encompassing multiple stages such as
vulnerability exploitation, lateral movement, command and control, and
exfiltration. Planning can adapt if the attack fails at any stage,
necessitating reevaluation and adaptation of acquired observations and
gathered information.

An example of the operation-level games is described in [105]. A multi-phase
and multi-stage game is used to capture the attack vectors of advanced
persistent threats. Each phase and each stage has distinct characteristics and
requires a different form of defense strategy. A dynamic game framework can
piece together games at each phase and each stage to capture the whole attack-
and-defense operation holistically from the entry point to the target. A more
sophisticated dynamic game that incorporates incomplete information and cyber
deception has been presented in [46] and [45]. It depicts long-term dyadic
interaction between a stealthy attacker and a proactive defender through a
multi-stage game of incomplete information. Each player holds private
information unknown to the other, and strategic actions are guided by beliefs
formed through multi-stage observation and learning processes.

The game at the tactic level is represented by the short-term local
interactions between an attacker and a defender. Each stage of the operation
involves a distinct type of dyadic interactions. For example, in the social
engineering game at the reconnaissance stage, the attacker can exploit the
cognitive vulnerabilities of the defenders to gain initial access. The
attacker often has an information advantage when it aims to deceive the
defender. At the stage of lateral movement, the defender can guide the
attacker to a honeypot so that the attack will be detected and revealed. This
defensive deception provides the defender information advantage at the stage
of the game. Hence, throughout the operation, the game can take different
forms depending on the structure of information, interactions, and
maneuverability. The survey in [77] explores game theory frameworks designed
to model defensive deception strategies in cybersecurity and privacy domains.
It introduces a taxonomy comprising six distinct types of deception:
perturbation, moving target defense, obfuscation, mixing, honey-x, and
attacker engagement. These classifications are characterized by their
information structures, agents involved, actions taken, and duration, all of
which align closely with game theory concepts. This taxonomy establishes a
structured framework for comprehending the diverse strategies of defensive
deception. The survey outlined in [68] offers a curated selection of studies
that demonstrate the application of game theory in addressing various security
and privacy challenges within computer networks and mobile applications. In
each domain, we identify security problems, players, and GMs, including
security of the physical and MAC layers, security of self-organizing networks,
intrusion detection systems, anonymity and privacy, economics of network
security, and cryptography. The games that describe the local interaction can
be viewed as a building block to synthesize an operational level game, and
hence informing the creation of the strategic level games.

The multi-level interdependencies among the three levels of the games are
illustrated in Fig. 1. The required granularity of the GMs differs across
levels. The strategic-level models are long-term and require a high-level
description of potential operation consequences once resources are utilized.
The outcome of the strategic-level Blotto game can be predicted by an
operational-level game simulator. The tactical-level models require higher
precision, as precision is crucial for determining the exact actions to be
taken at the focused stage. The tactical-level games are driven by the high-
level objectives specified at the strategic level. Hence, inherent
interdependencies exist among the three layers of the games. The tactical ones
inform the consequences of the strategic ones, while the strategic ones
specify the objectives, constraints, and structures of the tactical games. The
operational ones reside in the middle layer, serving as an intermediary that
interconnects both ends.

It can be observed that cyber warfare games are multi-scale and multi-
resolutional. Zooming in from the strategic level to the tactical level is a
top-down process that specifies elements of the tactical games. Conversely,
zooming out from the tactical level to the strategic level is a bottom-up
process. The outcomes of individual tactical games and their compositions lead
to the prediction of strategic level interactions and inform strategic level
decisions. The zooming-in and zooming-out process can be adaptive. When
strategic-level decisions change, the tactical level needs to adapt to the
change in an agile manner. If tactics fail due to uncertainties, unexpected
events, or errors, resulting in operational-level task failures, there is a
need to resiliently adjust strategic-level decisions. This adjustment allows
for the design of and adaptation to new missions to recover from the failure
and ensure defense.

Accompanied by the ability to zoom in and out, new solution concepts beyond
equilibrium are necessary to predict game outcomes across various levels and
resolutions. These concepts must be compatible with uncertainties, limited
observations, and the non-stationary nature of interactions. Hence,
nonequilibrium solutions are essential to address these features, aiming to
create a reasonable prediction even though the outcome of the game can be
stochastic with limited rounds of interactions. Moreover, solutions for
tactical-level games must be consistent with those at the strategic level,
despite differences in scales or levels of detail. This consistency represents
another dimension of consistency, in addition to conjectural and incentive
consistencies (e.g., associated with the solution concepts Berk-Nash
equilibrium [24], Nash equilibrium [70]), leading to a holonic solution where
localized tactical games consistent with global strategic ones.

The new equilibrium concepts play a crucial role in assessing the risk of the
overall mission. Mission risk is inherently multi-scale; risks at the tactical
level can impact those at the strategic level. Moreover, planning decisions’
risks at the strategic level can influence the selection of tactical level
strategies. High-level risks can impose constraints on low-level strategies
and guide their decision-making process. Conversely, low-level risks can
propagate and manifest as high-level risks. Computational tools associated
with solution concepts at each level must be integrated to create a cohesive
tool capable of automated, coordinated, zoom-in, and zoom-out risk analysis.

Learning and adaptation are crucial aspects of the solution framework. Rather
than viewing equilibrium solutions as defining the learning process, we must
reconsider and understand that learning processes shape game outcomes.
Learning serves as a natural descriptor of gameplay, alongside strategic and
extensive form game descriptions. This description can result in equilibrium
and non-equilibrium outcomes depending on the time horizon examined.

The learning description of the game facilitates the development of adaptation
schemes for games at multiple levels, as adaptation can be directly and
descriptively designed rather than being considered a derivative of
equilibrium analysis. Just as solution concepts associated with multilevel
learning need to be consistent, adaptation across levels must also exhibit
consistency. Firstly, adaptation must exhibit top-down causality, where
adaptation at the tactical level may be triggered by uncertainties or
unexpected events at its own level and by adaptation at the strategic level.
Secondly, adaptation must be coordinated and stable. Multilevel adaptation
requires coordination to avoid scenarios where adaptation at one level causes
more failures or leads to cyclic or unstable outcomes.

###  2.2 FM-Enabled GMs

The perspective described above delineates a new research direction aimed at
developing programmable and mosaic game-theoretic models along with a range of
versatile methods to advance the design of decision-dominant defense tactics
and strategies to prevail in cyber warfare. The initial phase involves
establishing a library of tactical games as foundational components. These
tactic games serve as fundamental building blocks that encapsulate the typical
adversarial situations encountered by defenders. They encode the defender’s
knowledge regarding feasible actions and potential attack responses using
various representations, including strategic form games, extensive form games,
and learning form games.

Strategic and extensive form games have traditionally been discussed in
textbooks. For instance, a simple rock-paper-scissors game can be depicted
using a matrix, which is a form of strategic representation. Meanwhile, a
stochastic dynamic game with multiple stages of interactions can be
represented using a tree structure that illustrates the multi-round
interactions among players, their observations, and the uncertainties inherent
in decision-making. The learning form game represents a novel approach,
specifying how agents respond to and learn from acquired information and
knowledge. It eliminates the necessity to utilize utility functions to define
players’ objectives or incentives. Instead, players’ objectives are implicitly
conveyed through dynamic learning processes wherein they adapt their
strategies toward long-term goals. These goals are expressed through sequences
of strategy updates, potentially leading to either equilibrium or non-
equilibrium outcomes. The learning representation facilitates the translation
of observed player behaviors into learning patterns, which may be
nonstationary. The uncertainty quantification of behaviors using learning
represents a promising avenue for bridging theory and practice. Furthermore,
the GMs offer immediate adaptability, an inherent property of learning
dynamics. Moreover, the way in which players learn can also adapt to
contextual or environmental changes.

A tactical game is designed to be composable with others. This composability
can result in a larger game, leading to a multi-phase and multi-stage
operational game that describes a more complex cyber operation [105].
Composability can take on different forms: sequential, expansive, or
reinforcing. Sequential composability forms a sequential game where the
scenario of one game is followed by that of another. It allows the defender to
prepare for forthcoming interactions and make informed defense decisions
before the scenario changes, potentially shifting the advantage from the
defender to the attacker. Expansive composability involves aggregating two
games into one larger game with a more complex structure of action spaces,
dynamics, or information structures. It can be viewed as a parallel
composition where players engage in two scenarios simultaneously. This enables
the defender to confront an attacker with augmented capabilities or multiple
attackers coordinating to achieve their goals. Reinforcing composability is a
type of feedback composability where the outcome of one game affects the
outcome of the other and vice versa. It captures gameplay in which one cyber
scenario influences another and eventually returns to itself. When the
feedback has a negative impact, the defender faces a vicious cycle where
failure leads to further losses in the same scenario.

The canonical forms of composability enable the game framework to be both
mosaic and adaptive. By combining two composable games, defenders can
effectively analyze and strategize against attackers. Moreover, as contexts or
strategic objectives evolve, these games can be reconfigured or recomposed to
align with new missions. This flexibility is particularly crucial during
operational setbacks, where swift adaptation is vital for strategic
resilience. Such adaptability introduces a novel capability for defenders in
cyber warfare, and it can be further strengthened by advances in FMs that
facilitate online learning and knowledge representation.

The development of tactical games and their ability to compose, reason, and
learn is not limited to online response and interactions with adversaries.
Another advantage lies in the development of game-theoretic digital twins
capable of simulating hypothetical scenarios and predicting outcomes
previously unencountered. The capabilities of game-theoretic digital twins can
inform strategic-level decision making, allowing comprehensive planning by
evaluating risks associated with both familiar and unfamiliar scenarios, and
the reasoning of an optimal mission-driven strategy. Furthermore, at the
tactical level, the game-theoretic digital twin can be also used to create
conjectures or predictions of the adversarial behaviors, allowing the defender
to gain preparatory advantage over the attacker and improving the tactical
decision dominance.

Learning and adaptation occur at multiple levels, forming several adaptation
loops. Strategic-level adaptation must coordinate with associated adaptations
at the tactical level. A rapid top-down translation between strategic-level
mission goals and tactical-level tactics is necessary to enable agile
responses to changes in the continually evolving threat landscape in
cyberspace. This translation necessitates different levels of knowledge
representation. At the strategic level, knowledge and information are encoded
as semantic objectives, rules, constraints, and feasible sets. At the tactical
level, knowledge and information are represented by acquired spatio-temporal
observations encoded in numerical values, time-series data, and binary
outcomes. Neurosymbolic learning, which integrates symbolic reasoning with
data-driven learning, is essential to facilitate top-down and bottom-up
coordination of responses to heterogeneous knowledge and information generated
at different levels and from different sources.

This translation operates in both directions. Apart from the top-down impact
of knowledge on tactical decisions, new knowledge generated at the tactical
level can significantly influence decisions at operational and strategic
levels. The propagation of knowledge, both bottom-up and top-down, requires
careful study. It demands symbolic learning mechanisms operating at multiple
scales to effectively disseminate insights and optimize decision-making
processes. To support these investigations, there is a need to establish new
solution concepts along the way. Non-equilibrium and learning-based solution
concepts are essential for describing the outcomes of multi-level games. These
solutions must demonstrate consistency across levels, while the learning
process should be causal, coordinated, and stable.

FMs allow a more powerful way to achieve the above. They enhance the learning
capabilities of each game building block, particularly in tactical games where
higher resolution payoffs, information, and dynamics are required. FMs excel
in understanding information from diverse sources, including textual,
semantic, and numerical data, facilitating the fusion of information and
enhancing game resolution through FM-enabled analytics.

Moreover, FMs facilitate the synthesis of GMs. FMs can automate the
integration and synthesis of operational games by selecting and fusing
relevant sets of tactical games. Additionally, they provide a concise and
high-level depiction of strategic-level games for decision-making purposes,
akin to how LLMs summarize information and grasp its essence.

FMs can also play a role in the coordination of learning and adaptation across
the layers. Reinforcement learning enabled by the FMs can provide augmented
capabilities for adaptation and learning, leveraging the multi-source and
multi-modal time-series information. To achieve this, new architectures
involving FMs and GMs are needed to achieve cross-level coordination and
adaptation.

Fig. 4 illustrates the fundamental architectures of the FMs with GMs. A GM can
be supported by an FM to identify the game through the learning of the
incentives, information structure, and dynamics of the players and provide a
more accurate representation of the interactions between the players. This
relationship has been depicted in Fig. 4(a). Two GMs can also be integrated to
create a meta-game through an appropriate FM. This process creates
operational-level games from the game building blocks at the tactical level.
This architecture is illustrated in Fig. 4(b). Illustrated in Fig. 4(c), the
sequential adaptation and coordination between two GMs, each supported by
their FMs, are essential to create tactical level resiliency when encountering
uncertainties and time-varying environments. The coordination between the two
stages at the tactical level improves the efficacy of the operation. When the
mission changes, the operation needs to adapts too. The adaptation of an
operation meta-game can be enabled by an FM, which not only reacts to the
changes in the mission and outcomes of the tactics but also coordinates the
learning at the tactical levels. This cross-level architecture is depicted in
Fig. 4(d).

Figure 4: Examples of Architectures of Symbiotic FMs and GMs: (a) FM $F_{1}$
enriches GM $G_{1}$ by improving the precision of the GM and augmenting its
learning capabilities; (b) Tactical games $G_{1}$ and $G_{2}$ are fused
together to achieve an operation game through the FM; (c) The adaptation of
two sequential tactic games $G_{1}$ and $G_{2}$ is enabled by FM $F_{1}$ and
$G_{2}$. They are coordinated sequentially; (d) The operational level game
learning $F_{3}$ coordinates the learning of $F_{1}$ and $F_{2}$.

##  3 Foundation Models and Large Language Models and the Synergetic Roles in
Cybersecurity

FMs refer to machine learning models that are trained on broad data, generally
using self-supervision at scale, such that they can be adapted to a wide range
of downstream tasks. FMs differ from existing machine learning (ML) models in
two aspects: scale and scope. Scale: FMs generally feature large-scale neural
network models with an astronomical number of parameters to be determined by
self-supervised training over comparable data. For example, GPT-3, an FM in
natural language processing, has 175 billion parameters and is trained on 45TB
of text data. Scope: FM, as a generalist, aims to handle multi-modal data and
perform a wide range of tasks without being explicitly trained to do so. It is
observed that FMs possess few-show generalizability: a handful of
demonstrations from new tasks are sufficient for FMs to adapt. In contrast, ML
models are specialists, targeting specific tasks and acting on certain types
of data, such as image classification. They typically suffer from poor
generalization when transferred to tasks unseen in the training stage. In
summary, FMs are large-scale generative models with highly resource-intensive
pretraining, capable of learning general features and patterns from diverse
data sources. Examples of FMs include large language models (LLM) for natural
language processing [72], DALL-E for images[78], MusicGen for music [22], and
RT-2 for robotic control [110].

Figure 5: The encoder-decoder structure of the Transformer architecture,
adapted from [87]. Each input datapoint, after embedding and positional
encoding, is fed to the attention module in the encoder part (the right half),
which extracts temporal correlation (attention scores) across the input
datapoint sequence. The attention scores are then passed to the decoder (the
left half) to generate an output sequence auto-regressively, together with
additional attention within the output sequence. The attention mechanism is
instrumental in descriptive, predictive, and perspective analytics in
cybersecurity.

The few-shot generalization ability of FMs stems from the attention mechanism
in the transformer architecture [87] shown in Figure 5, which effectively
captures long-range temporal dependencies among inputs. As the building block
of FMs, the transformer consists of an encode (on the left half) and a decoder
(on the right half). The task of the encoder is to map an input sequence from
multi-modal high-dimensional data sources to a sequence of latent
representations in a unified vector space, which is then fed to the decoder.
Upon receiving the encoder’s output, the decoder generates a new output based
on its previous outputs, producing an output sequence in an auto-regressive
manner. Mathematically, denote the input sequence by
${\mathbf{x}}=\\{x_{1},x_{2},\ldots,x_{n}\\}$, which, for example, can be a
sentence to be translated or a sequence of sensor readings for robot controls.
The transformer is a parameterized auto-regressive probabilistic model
$\mathcal{P}_{\theta}$ that consumes the input $\mathbf{x}$ and generates an
output sequence $\mathbf{y}=\\{y_{1},y_{2},\ldots,y_{m}\\}$ using previously
generated outputs, i.e.,
$y_{t}\sim\mathcal{P}_{\theta}(\cdot|y_{t-1},\ldots,y_{1};\mathbf{x})$.

Each input datapoint $x_{i}$ to the transformer, which we will call a token,
is initially embedded in vectors of a certain embedding dimension with
additional positional encoding so that each position in the input sequence
acquires a unique representation. Each input embedding generates a query, key,
and value vector of dimensions $d_{k}$, $d_{k}$, and $d_{v}$. Vectors of the
same type are stacked column-wise to produce three matrices
$Q\in\mathbb{R}^{n\times d_{k}}$, $K\in\mathbb{R}^{n\times d_{k}}$, and
$V\in\mathbb{R}^{n\times d_{v}}$, with $n$ being the length of the input
sequence. The attention score is then calculated with the formula

$\text{Attention}(Q,K,V)=\text{softmax}\left(\frac{QK^{\intercal}}{\sqrt{d_{k}}}\right)V.$

The matrix $QK^{\intercal}$ is divided by $\sqrt{d_{k}}$ to prevent the
vanishing gradient problem when applying the soft-max row-wise [87]. The
entries of the resulting attention matrix represent the correlation among
input tokens. Using the translation example, each entry captures how the word
to be translated relates to others in the sentence. Both the encoder and
decoder rely on the attention mechanism for correlation extraction in the
original sentence $\mathbf{x}$ and the translation $\mathbf{y}$, respectively.
Yet, their usage of attention bears a subtle difference. The upper off-
diagonal triangle part of the resulting matrix
$\text{softmax}({QK^{\intercal}}/{\sqrt{d_{k}}})\in\mathbb{R}^{l\times l}$ is
masked with 0s in the decoder part. This causal mask prevents future tokens
from influencing the prediction of the current output and is the defining
feature of a causal transformer, distinctive from other variations.

To allow the attention mechanism to extract correlation from different
representations, FMs often utilize multi-head attention where queries, keys,
and values are linearly projected multiple times (one projection corresponds
to one head attention) with different learned projections to $d_{k}$, $d_{k}$,
and $d_{v}$ dimensions, respectively. The attention mechanism reviewed above
acts on the projection in parallel, producing $d_{v}$-dimensional values to be
concatenated into a single final value, as shown in Figure 5. The positional
encoding and generation of $Q$, $K$, $V$ matrices, together with feed-forward
networks and linear layers in the transformer, are trainable components. The
parameter size soars up and easily attains the billion level for recent FMs
[72], as the embedding dimension, context length, and number of heads
increase.

The attention mechanism is the cornerstone of FM’s generalization when
performing downstream tasks. The key observation is that the correlation is
invariant across various sequential data, and the attention score acquired in
pre-training lends itself to a variety of game-theoretic security analytics
across various dimensions presented below.

###  3.1 Descriptive Analytics

FMs demonstrate their use by harnessing historical data to construct a formal
description of game scenarios, capturing the dynamics, incentives, and players
involved in the interactions. For instance, drawing upon past experiences,
these models can create a matrix game that encapsulates the competitive
interplay between an inspector, employing randomized examinations to identify
attackers, and the agile attacker, adept at evading scrutiny. This descriptive
analytics framework captures the essence of the evolving interactions within
security games.

Another emerging game-theoretic security paradigm brought by this descriptive
analytics is the natural game representation. Unlike the matrix and other
standard game representations in the cybersecurity context, the natural
representation features an end-to-end treatment of the actual network systems
through FMs and, in particular, large language models (LLM) as the prevalent
data in cybersecurity are of text type. LLMs are capable of summarizing
evidence-based insights from lengthy cyber threat intelligence (CTI) texts and
deriving semantic knowledge from CTI [79], which serves as the game state.
Thanks to the attention mechanism, LLMs can discover the correlations between
vulnerabilities and attack patterns, mapping Common Vulnerabilities and
Exposures (CVE) to CommonWeaknesses Enumeration (CWE) [23] and linking CVEs to
MITRE ATT & CK techniques [32]. Such LLM-based mapping naturally specifies the
attacker strategy space without undergoing mathematical modeling. The end-to-
end security pipeline centered around LLMs and FMs is projected to take an
increasing share in cybersecurity task automation.

###  3.2 Predictive Analytics

The predictive capabilities of FMs extend to anticipating the forthcoming
games and deciphering the strategies likely to be employed by adversaries.
Given the nonstationary nature inherent in many applications, predictive
analytics serves as a strategic tool for gaining an intelligence advantage. By
inferring patterns and trends from past interactions, FMs facilitate proactive
decision-making, ensuring defenders are well-prepared for the next move in the
dynamic landscape of security games.

FMs’ predictive power proves to be instrumental in predictive reinforcement
learning in the cybersecurity context [35], where the policies are updated
online according to the defender’s forecast of the future consequences and
anticipation of the attacker’s reactions. Unlike offline or batch
reinforcement learning [3], this predictive learning paradigm emphasizes the
learning agent’s online adaptability to a subjective forecast of future
environment evolution and opponent [58]

Two primary challenges arise from the predictive learning paradigm, to which
FMs offer a unified data-driven approach. The first is to adapt the policy on
the fly to the forecast with lightweight computation. Existing efforts utilize
the multistep lookahead idea whereby the agent predicts multiple rounds of
possible interactions (trajectories) in the future [59, 35]. A policy
improvement is then carried out by seeking the optimal policy maximizing the
cumulative utilities within the lookahead horizon. As pointed out in [59],
such a lookahead optimization is more involved than vanilla policy
optimization. The adapted policy shall only target a set of plausible
forecasts, i.e., those close to the actual trajectory evolution, while
discarding all other candidates with marginal probabilities. Consequently, the
lookahead adaptation boils down to constrained stochastic optimization,
requiring sophisticated machinery for efficient computation.

FMs, as a generative model, naturally fit the role of the predictor in
generating future trajectories. Unlike the Monte Carlo simulation that is
commonly used in existing works [35, 58], FMs can extract the temporal
correlation among past interactions via attention scores and apply them to
generate new forecasts without explicitly modeling the environment, leading to
high-resolution model-free predictions that are indistinguishable from actual
trajectories [52]. The high-accuracy predictions pave the way for online
planning algorithms, such as Monte Carlo tree search and rollout methods
considered in [59] and [35].

The second challenge pertains to the agent’s subjective perceptions of the
environment and the opponent, based on which it makes forecasts. The agent
needs to calibrate its subjective conjecture on the environment dynamics [35]
and the opponent’s strategy [58] using the online information feedback, e.g.,
observations. Such a calibration process, performed also online, aims to
ensure consistency between the learning agent’s subjective perceptions and the
objective multi-agent decision-making [58]: what one observes does not
contradict what one believes. To ensure consistency, existing works resort to
Bayesian learning approaches, inspired by Bayesian parametric statistics [59,
35, 58]. The proposed Bayesian learning begins with a parametric
representation of external uncertainties regarding the environment and the
opponent: a set of parameterized models is available to the learning agent,
each of which represents a possible system dynamics and opponent strategy.
Starting with a prior distribution over these models, the agent continuously
updates the posterior upon receiving information feedback, which proves to
concentrate asymptotically on the models closest to the actual environment
dynamics and opponent response [35, 58].

FMs can revolutionize the calibration process in predictive reinforcement
learning. To begin with, it is natural to treat different FMs as parametric
models in Bayesian learning, with each pre-trained on different data sources
capturing various temporal correlations in system trajectories and opponent
sequential actions. Beyond such a straightforward extension, FMs can directly
cater to the calibration process in a model-free manner, as investigated in
[57]. Without building parametric models beforehand, FMs cut straight to the
opponent’s action sequence predictions (forecasts), which are then fed to FMs
again to generate the ego agent’s actions conditional on its predictions. The
calibration takes place implicitly in the transformer’s auto-regressive
operation: the updated forecasts depend on the previous predictions and the
information feedback. Recall that the transformer corresponds to a
probabilistic model
$y_{t}\sim\mathcal{P}_{\theta}(\cdot|y_{t-1},\ldots,y_{1};\mathbf{x})$. In the
context of predictive reinforcement learning, $\mathbf{x}$ denotes the past
information feedback and the output
$y_{t}:=(\widehat{s}_{t:t+K},\widehat{a}_{t:t+K},a_{t})$ includes the the
agent’s forecast of future $K$-step system evolution $\widehat{s}_{t:t+K}$,
the opponent’s action sequence $\widehat{a}_{t:t+K}$, and the agent’s best
response $a_{t}$ against predicted opponent’s moves.

More than a forecaster that generates future trajectories, FMs also assume the
roles of the actor (policy improvement) and critic (policy evaluation) in
reinforcement learning, leading to an integrated forecaster-actor-critic (FAC)
pipeline [58] embodied by the transformer. In contrast to model-based
predictive learning [35, 58], FM-powered FAC opens promising avenues to model-
free predictive reinforcement learning, exploring a rich class of
opponent/system modeling in a data-driven fashion, alleviating the model
misspecification in Bayesian learning [35].

###  3.3 Prescriptive Analytics

The prescriptive analytics in cybersecurity aims to provide targeted
recommendations for defense strategies, with the overarching objective of
minimizing the impact of potential attacks. FMs serve as a mechanism to
generate bespoke recommendations and solutions. These actionable insights
become invaluable resources for policymakers and network administrators. By
leveraging FMs, prescriptive analytics directly enhances the security
intelligence available to end-users and defenders. This strategic augmentation
ensures a proactive and informed approach to defense, equipping stakeholders
with the foresight and tailored solutions needed to mitigate risks
effectively.

The use of prescriptive analytics, together with descriptive and predictive
analytics, extends to the design of sophisticated learning algorithms. One
emerging paradigm that can benefit from FMs’ prescriptive capabilities is the
non-equilibrium learning [75, 74] and its associated learning defense. Unlike
conventional game-theoretic learning, non-equilibrium learning shifts the
focus from long-term equilibrium-seeking to transient strategic interaction
characterization. Such a paradigm shift is particularly relevant to
cybersecurity, where the defender must acquire an advantageous position within
a short window before the attack cyber kill chain materializes [60]. As
delineated in [75], the three pillars of non-equilibrium learning are the
target set (e.g., advantageous positions), the measurement function, and the
time window. A learning process is said to achieve non-equilibrium if the
measurement of the learning dynamics falls in the target set within the time
window. Compared with equilibrium-focused multi-agent learning, non-
equilibrium learning emphasizes finite-time approachability to a set of
desired outcomes [61]. Thanks to the measurement function, the approachability
evaluation in non-equilibrium learning is much more flexible than the utility-
driven one in standard game-theoretic learning, which takes into account
broader defense objectives than simply utility-maximization, such as privacy
and transparency preserving [77, 64].

The introduction of FMs to the cybersecurity domain enables an offline pre-
trained online adaptable prescription for non-equilibrium-based cyber defense.
Beginning with the offline pre-training, FMs first digest historical security
data, such as CWE, CVE, and system log files, through self-supervised
representation learning. The pre-trained FMs provide high-confidence
situational awareness of the network systems and adversarial behaviors, which
further translates to proper measurement functions producing accurate cyber
risk assessment and corresponding desirable outcomes for non-equilibrium
learning design.

Naturally, designing learning dynamics from scratch may take a prolonged
period, and the defense may completely miss the window of cyber advantage when
the defender takes charges before the attack cycle completes. A more viable
and effective defense prescription to achieve non-equilibrium is to consider
the meta-learning prescription, whereby the FMs first extract common defense
strategies or defense response patterns in the offline stage by consuming
diverse security data at scale. When deployed online, a handful of online
observations on the network system suffices for fast defense policy
adaptation, as FMs are decent few-shot learners due to the attention mechanism
[72]. The offline pre-trained defense is referred to as the meta-policy,
pertaining to a wide variety of security scenarios. As demonstrated in [28,
73], such as meta-learning prescription is scenario-agnostic in the sense that
FMs need not examine the exact system configuration. The online adaptation is
purely data-driven with marginal computational overhead, leading to effective
non-equilibrium defense under system uncertainties.

As we delve into these advanced methodologies, it becomes imperative to
reassess traditional equilibrium concepts that underpin our understanding of
game outcomes, as motivated by the non-equilibrium concept [75]. The
conventional objective has been to compute the equilibrium of the game, where
the player’s uncertainties regarding the environment and opponents are
internalized as incomplete information [69]. However, the advent of FMs, where
agents harness data in diverse ways to formulate strategies, challenges the
adequacy of solutions that internalize all uncertainties. Instead,
practicality dictates the exploration of solutions corresponding to models
that externalize uncertainties.

Consider predictive reinforcement learning with parametric models representing
internalized system uncertainties. In a case where no external uncertainties
are introduced, the firm conclusion is that the learning cannot exceed the
optimality under the given uncertainty modeling. Yet, such a claim only holds
for closed systems. In real-world applications, many uncertainties are not
modeled or are impossible to model precisely, which necessitates an open
system model with external uncertainties.

As such, the pursuit of equilibrium defense is no longer legitimate in
cybersecurity, due to the presence of externalities. In this context, the need
for novel solution concepts arises. As discussed in the preceding subsection,
the notion of consistency [58], inspired by the Berk-Nash [24] and self-
confirming equilibrium [26], offers a promising avenue for describing game
outcomes in models that explicitly externalize uncertainties, achieving superb
performance in reinforcement learning [57] and cybersecurity benchmarks [35].
In addition to consistency, another relevant notion is decision dominance
[60], where the dominant party refers to one who can extract information from
data and learn about external uncertainties. Whoever completes the information
acquisition and analysis cycle faster gains an information advantage over the
opponent on the external uncertainties. Unlike classical equilibrium defense
resting on the steady state of strategic interactions, decision dominance
defense focuses on establishing an information advantage within a transient
window and acting decisively before losing the initiative. This shift in
perspective acknowledges that not all uncertainties need to be explicitly
modeled within the game framework.

###  3.4 Foundation models for Mechanism Design for Security Games

The design of security games is another domain where FMs can contribute to
achieving given security objectives with underlying specifications. The
formulation of design problems is facilitated through hyper-FMs, wherein FMs
serve as fundamental building blocks for the design process. An illustrative
example involves the use of FMs by security game designers to determine
optimal game parameters, influencing the course of actions undertaken by the
involved agents. This process needs to use additional FMs to anticipate the
actions and behaviors of the agents.

Many components of interactions are amenable to design or control, including
incentives (player payoffs) [43], game dynamics (course direction shaped by
actions), and information disclosed to players during gameplay [92, 98]. The
design process itself can take either an offline or online approach. Offline
design involves training FMs to ascertain optimal game configurations, while
online design employs a reinforcement learning process that dynamically adapts
to player actions. Both approaches leverage hyper-combinations of analytics
through FMs or the design of hyper-FMs to achieve their objectives.

##  4 Cyber Deception Game and Foundation Models

There are several quintessential domains in which FMs can play a significant
role in cyber deception. Cyber deception operations involve numerous tactical
components, including information gathering, detection and response,
configuration and deployment of honeypots, and engagement with attacks. In
this section, we specifically discuss the connection between FMs and GMs in
the use of defensive cyber deception for attack engagement and defensive
response. Once an attacker is in the network, the goal of defensive cyber
deception is to thwart and mislead the attacker who are attempting to breach
or infiltrate the network or systems by deploying techniques such as fake
credentials and honeypots to deceive and divert attackers’ attention away from
valuable assets and towards simulated or less critical targets. Many game-
theoretic approaches have been proposed to describe various scenarios, [77,
53]. For instance, a signaling game framework has been used to capture the
asymmetric information between the two players [76]. In [39], a one-sided
information stochastic game is used to examine the effects of deception on the
attacker’s belief. The study has explored the sequential nature of attacks and
investigates how an attacker’s beliefs evolve, influencing their actions. It
has demonstrated strategies for defenders to manipulate attacker beliefs
effectively, hindering attackers from achieving their objectives and
minimizing network damage.

###  4.1 Challenges in Cyber Deception

One key challenge inherent in cyber deception lies in understanding attacker
behaviors through proactive engagements. It is crucial to deduce the
incentives and motivations driving attackers by leveraging heterogeneous
sources of data, including traffic data, log data, and event data. By doing
so, defenders can gain insight into TTPs used by the attackers and their
objectives. It enables the defender to prescribe the most effective responses
to emerging threats.

The following is an example of the parsing of PCAP data that captures the
scenario when an attacker responds to the patching of network systems. Their
behavior may change as they adapt to the evolving security measures. The
attacker initially attempts to exploit known vulnerabilities in the target
system. However, as the target system patches these vulnerabilities, the
attacker’s exploit attempts become unsuccessful. The attacker responds by
continuing to probe the target for other potential vulnerabilities and, upon
identifying a successful attack vector, exfiltrates data to an external
server. This PCAP table illustrates an attacker’s adaptive behavior in
response to network system patching, highlighting their persistence and
ongoing efforts to exploit vulnerabilities and compromise the target
environment.

90  Frame Action Source Destination Protocol Flags 1 SYN packet sent
Attacker_MAC Target_MAC TCP SYN 2 SYN-ACK response Target_MAC Attacker_MAC TCP
SYN 3 Exploitation attempt Attacker_MAC Target_MAC TCP PSH ACK 4 Exploit
attempt unsuccessful Target_MAC Attacker_MAC TCP RST 5 SYN packet sent
Attacker_MAC Target_MAC TCP SYN 6 SYN-ACK response Target_MAC Attacker_MAC TCP
SYN ACK 7 Data exfiltration attempt Attacker_MAC External_Server_MAC TCP PSH
ACK 8 Data exfiltration successful External_Server_MAC Attacker_MAC TCP ACK

CAPTION: The presented PCAP table shows the adaptive nature of an attacker
encountering patched network systems. Initially, the attacker seeks to exploit
known vulnerabilities within the target system. However, as the target’s
vulnerabilities are patched, the attacker’s exploit attempts are thwarted.
Undeterred, the attacker adapts by persistently probing the target for
alternative vulnerabilities. Upon discovering a successful attack vector, the
attacker shifts tactics, opting to exfiltrate data to an external server.

A comprehensive understanding of the attacker’s response is pivotal for
defenders to formulate effective strategies and implement appropriate
defensive measures. Creating a robust strategy involves not only understanding
the attacker’s immediate actions but also anticipating their potential moves.
It requires the ability to agilely analyze the attacker’s behavior and
determine the most suitable course of action to mitigate the impact of the
intrusion.

The defense strategy entails several crucial steps. Firstly, defenders must
meticulously map out the attacker’s TTPs. This involves gaining insights into
the attacker’s modus operandi, including their preferred attack vectors,
tools, and methodologies. By understanding the attacker’s playbook, defenders
can proactively identify vulnerabilities and develop countermeasures to thwart
potential threats. Moreover, defenders must be adept at estimating the
possible trajectories of the attacker’s actions. This entails forecasting the
potential avenues that the attacker may pursue during the course of the
intrusion. By anticipating various scenarios and their associated risks,
defenders can better prepare for contingencies and respond effectively to
emerging threats. Central to the success of defense strategy is the ability to
act quickly and decisively. Defenders must be equipped to make rapid and well-
informed decisions in response to evolving threats. This requires leveraging
advanced technologies and methodologies to automate the decision-making
process and streamline response efforts.

FMs play a pivotal role in facilitating the learning process and empowering
defenders to navigate the complexities of cyber threats effectively. By
harnessing FM’s capabilities, defenders can gain valuable insights into the
attacker’s knowledge and intentions, enabling them to map out the cyber
landscape and identify potential vulnerabilities. Various types of FMs serve
distinct purposes in the intrusion response process. For instance, LLMs excel
at parsing and comprehending the nuanced nuances of the attacker’s intent,
enabling defenders to decipher malicious communications and identify potential
threats. Similarly, Decision Transformers [52, 20, 57] leverage sophisticated
algorithms and reinforcement learning techniques to predict attacker behaviors
and make optimal decisions in real time. By analyzing patterns and trends in
attacker activity, Decision Transformers empower defenders to anticipate
threats and implement proactive defense measures.

Apart from supporting the ability of the defender to use his knowledge to
predict the attacker’s paths, FMs can also be used to allow the defender to
synthesize and acquire knowledge over time. Understanding the attacker’s prior
behavior and potential scenarios is crucial for the defender to quickly update
its security policies. Proficient knowledge enables the defender to adapt
promptly and avoid extensive trial-and-error efforts. This knowledge is
typically encoded using symbolic representations of rules, laws, or
constraints. For instance, rules may be expressed through first-order or
temporal logic statements, while laws can be encapsulated in rule-of-thumb
equations, offering approximate responses. Constraints capture feasible
directions for updates, which can be weighted to prioritize specific
directions. Acquiring knowledge presents a challenge. One immediate method
involves knowledge sharing, where insights on unknown attacks can be gleaned
from those who have encountered similar incidents. In [27, 102, 103],
mechanisms for knowledge sharing among intrusion detection systems are
explored, introducing an incentive-compatible approach to encourage data
sharing and expedite responses to zero-day attacks. Alternatively, knowledge
can be synthesized from individual experiences and data. FMs play a pivotal
role here, encoding experiences and data into symbolic representations
conducive to formal reasoning, computation, and optimization of security
policies. Recent works in [89, 90] provide promising approaches of using FMs
to synthesize knowledge from datasets.

Another challenging area of cyber deception is the configuration and
utilization of honeypots in engaging attackers to acquire information and
knowledge. Honeypot games have been used to formalize the deployment and
configuration decisions by taking into account the adversarial interactions
and the engagement goals. For instance, in [44], a reinforcement learning
algorithm is proposed to map out an attacker’s behavior. The engagement has to
interact with the attacker, making sure that the attacker does not exist in
the honeynetwork. By observing and analyzing attacker interactions with
honeypots, defenders gain valuable insights into emerging threats and attacker
behaviors. There is a tradeoff between learning the attacker’s behaviors and
removing the attacker directly. The knowledge of attackers can be useful to
further protect ourselves from zero-day attacks in the future. However,
removing the attackers directly can lead to fewer risks.

Despite extensive research on honeypot games in both academic and practical
domains, a noticeable gap persists between the game-theoretic solutions
proposed in the literature and the practical requirements for effective
defense mechanisms. A significant challenge lies in the necessity for decision
dominance in decision-making processes. This means the defender must make
faster, better-informed decisions to safeguard the network effectively. To
achieve this, it becomes imperative to leverage both offline knowledge
databases about the attacker and online observations of attacker behavior to
predict their capabilities, moves, and incentives. FMs are capable of
generating different attack scenarios. By leveraging these scenarios, the
defender can better prepare for potential outcomes and develop proactive
deception tactics by simulating them and making decisions based on the
simulated outcomes. By doing so, defensive decisions can account for various
contingent scenarios, minimizing risks, and maintaining decision dominance.

###  4.2 A Neurosymbolic Learning Approach to Cyber Deception

In this context, the framework of neurosymbolic learning emerges as a
promising approach. This framework integrates multiple FMs to form a cohesive
system capable of learning from heterogeneous data sources and making informed
decisions regarding attacker engagement strategies. By incorporating
neurosymbolic learning techniques, defenders can enhance their ability to
adapt proactively to evolving threats and effectively defend against
sophisticated cyberattacks. Illustrated in Figure 6, the defender conjectures
the attacker’s tactics $t_{i}$ and policies $a_{i}$ at each step $i\in T$.
Based on the conjectures, the defender designs an optimal policy update
$d_{i}$ to adapt its defense action $u_{i}$ at each step $i\in T$. The multi-
stage rounds of interactions correspond to a sequence of tactical-level games.
As the environment and the operational level objective change, the tactical-
level games need to adapt. This change is captured through a contextual
parameter $\theta_{i}$, which learns from the heterogeneous sources of data
and adapts itself to identify the exact context so that the right set of
tactical games can be picked to design the security update policies. The
update of $\theta_{i}$ is at an operational level, which has a different time
scale from the tactical level. Let $\bar{T}$ be the set of time steps, which
leads to a sequence of updates at a slower frequency in comparison with the
one associated with $T$. The contextual update policy is denoted by
$D_{i},i\in\bar{T}$. Its learning is driven by information from online
monitoring of the attack behaviors and network changes, and inputs from the
operation and strategic levels. Each context $\theta_{i},i\in\bar{T}$
corresponds to a knowledge set $K_{i},i\in\bar{T}$, which includes the rules
of engagement, system constraints on security policy adjustments, permissible
conjectures, and patterns for updating policies. The knowledge set affects the
way how the defender conjectures the attacker and adapts the security policy
at the tactical level.

FMs serve as pivotal tools across various functions including reinforcement
learning, knowledge assimilation, formation of conjectures, and contextual
representation. Moreover, they facilitate the coordination of multiple
components in the neurosymbolic learning. Figure 7 further illustrates the
synergy between FMs and GMs for cyber deception. A sequence of tactical games
$G_{1},G_{2},G_{3}$ unfold between an attacker and a defender. The defender
leverages $F_{1}$ to conjecture the attacker’s behavior and utilizes $F_{2}$
to adapt security measures based on acquired observations. This conjecture and
subsequent updates stem from the defender’s knowledge, which is symbolically
represented using $F_{4}$.

Driving the conjectural learning process is $F_{5}$, coordinating the
evolution of conjectures and policy updates. The tactical game unfolds
iteratively, driven by operational-level objectives. Environmental shifts and
operational goals require further adaptations in the tactical gameplay.
Contextual parameters denoted by $\theta$ capture these changes. $F_{3}$
processes diverse data sources to identify contextual changes, while $F_{6}$
bridges tactical gameplay with contextual shifts. Each context $\theta$ has an
associated knowledge set $K$, which dynamically updates in response to
contextual changes. FM $F_{7}$ provides a set of rules for policy updates and
conjecture formation under a context. FM $F_{4}$ is used to figure out the set
of relevant knowledge which $F_{7}$ can choose from. $F_{4}$ can also create
new rules for new contexts transferrable from other contexts or learned from
datasets.

The multi-scale perspective of neurosymbolic learning aligns with the multi-
level representation of security games. Contextual and knowledge updates at
the broader time scale correlate with operational-level games, which adapt to
changes in mission and environment. The symbiotic interaction between GM and
FM at this level fosters operational-level resilience. Conversely, security
updates and attacker conjectures at the finer time scale correspond to
tactical-level games, facilitating comprehensive adversarial reasoning and
tactical responses. The symbiotic relationship between GM and FM at this level
fosters tactical-level agility. Integrating these elements confers a decision-
dominant advantage, providing both agility and resilience for the mission.

Figure 6: Multi-agent neurosymbolic learning enabled by GMs and FMs: The
defender conjectures the attacker’s behavior and policies $a$ and finds the
optimal security policy update $d$ at each round of tactical interaction
between the two players. The defender updates the context parameter $\theta$,
which captures the contextual information, including the operation level
information and the environmental information. Each context is associated with
a knowledge set, which includes a set of rules of the game, including the
system constraints on the security policy updates, the admissible set of
conjectures, and learning patterns to update the policy updates. FMs are used
for reinforcement learning, knowledge acquisition, conjectural formation, and
representation of contextual information. In addition, FMs are used to
coordinate the building blocks. Figure 7: Interconnections between FMs and GMs
for cyber deception: The tactical games are played between an attacker and a
defender. A defender uses $F_{1}$ to conjecture the attacker’s behavior and
uses $F_{2}$ to update the security knowledge. The conjecture and the update
are based on the knowledge of the defender. The knowledge is symbolically
represented and captured using $F_{4}$. The conjectured learning is driven by
$F_{5}$, which coordinates the conjecture update and the policy update. The
tactical game is sequentially played over time to achieve its operational-
level objective. The changes in the environment and the operational-level
objective can lead to the adaptation of tactical-level games. This change is
represented by the contextual parameter $\theta$, which requires $F_{5}$ to
process heterogeneous data sources to identify the context and $F_{6}$ to
coordinate between the tactical level games and the contextual changes. Each
context has an associated knowledge set $K$, which updates itself when the
context changes. FM $F_{7}$ provides a set of rules for policy updates and
conjecture formation under a context. FM $F_{4}$ is used to figure out the set
of relevant knowledge which $F_{7}$ can choose from. $F_{4}$ can also create
new rules for new contexts transferrable from other contexts or learned from
datasets.

###  4.3 Emerging Challenges

The practical implementation of security games encounters additional system
constraints specific to the domain, hardware, and user requirements. Solutions
must be tailored to these constraints, considering factors such as response
time, ethical defense actions, temporal sequences, and hardware complexity for
online learning. To address these constraints, FMs can be imposed during the
training or design phase, for instance, hardware-related ones.

For certain constraints, especially logical ones, FMs can be employed to
create discriminators capable of vetoing recommendations that do not align
with a learned criterion specific to the application setting. This transition
from a general-purpose security game to a specific-purpose one is achieved
through transfer learning using an appropriate architecture of hyper-FMs.

Despite these promising directions, challenges persist. The foremost challenge
is the scarcity of security data, creating the need for the amalgamation of
domain knowledge, FMs, and agent simulators to fulfill design goals. The
incorporation of system vulnerabilities, application workflows, and common
attacker behaviors into the design process becomes crucial.

Another significant challenge revolves around ensuring high confidence in
analytics and design. Given that security applications often pertain to
mission-critical scenarios, the trustworthiness and reliability of utilizing
FMs become paramount concerns. Strategies to address this challenge include
the development of adaptive or tunable FMs and the establishment of feedback
mechanisms, both contributing to achieving improved reliability in security
analytics and design.

Another practical challenge arises from the inference time current FMs consume
for outputting the next token. In the presence of advanced adversarial
attacks, and in particular, cyber threats, real-time inference is the
prerequisite of a rapid defense response to counteract attackers’ swift moves,
for example, lateral movement within the system. Accelerating the FM’s
inference with long contexts is imperative for predictive and prescriptive
security analytics.

##  5 Conclusions

Cyber deception operations are increasingly prevalent in today’s cyber
warfare, aiming to thwart and deter resourceful and intelligent attackers from
targeted assets. They utilize decoys, honeypots, and misinformation to
manipulate adversaries’ behaviors and decision-making processes. This chapter
investigates the relationship between game models (GMs) and foundation models
(FMs) for cyber deception. On one hand, GMs symbolically encode nominal
knowledge of interactions between attackers and defenders. The game-theoretic
representation, in strategic, extensive, or learning forms, encapsulates
knowledge and experience of attack models and potential defense outcomes. On
the other hand, FMs are baseline machine learning models providing powerful
tools to process and extract information from heterogeneous data, including
unstructured text data such as risk reports, regulatory documents, and
incident reports. They enable predictive decision-making by simulating and
generating known or unknown scenarios based on historical and current data,
facilitating proactive and adaptive responses to attackers online. GMs and FMs
can be symbiotically integrated to achieve multiple cyber defense functions,
leading to guardware that transforms network security. These building blocks
can be integrated through diverse architectures for descriptive, prescriptive,
and predictive analytics for applications at tactical, operational, and
strategic levels of the mission. This chapter proposes a multi-agent
neurosymbolic reinforcement learning paradigm integrating GMs and FMs into one
learning-based framework. It advocates for the capabilities of predictive
intelligence, symbolic reasoning, and knowledge update in defensive cyber
deception. Despite challenges in FMs and their integration with GMs, this
chapter provides a promising path toward cyber resilience and decision
dominance in cyber warfare.

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