arxiv: 2605.09415 · v2 · submitted 2026-05-10 · 💻 cs.AI

Recognition: no theorem link

Strategic commitments shape collective cybersecurity under AI inequality

Adeela Bashir , Zia Ush Shamszaman , Zhao Song , The Anh Han

Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:32 UTC · model grok-4.3

classification 💻 cs.AI

keywords cybersecurityAI inequalityevolutionary gamesstrategic commitmenttargeted subsidiescollective defensesystem resiliencesocial learning

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The pith

Subsidies for a small group of committed defenders can spread strong protection and cut successful attacks even when AI tools are costly for most.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

When advanced AI defense tools carry high costs, populations evolve toward cheap weak defenses that leave systems vulnerable to ongoing attacks. The paper builds an evolutionary game model in finite populations to show how a few committed defenders who always pick strong protection can influence others through imitation, yet costs still prevent stable security. Adding a targeted subsidy that removes the cost penalty for those committed players drives higher adoption of strong defense, suppresses attacks, and raises overall resilience while limiting attacker gains. Simulations across wide parameters confirm subsidies outperform commitment without support.

Core claim

When high-capability defense is costly, the population is driven toward low-cost weak-defence behaviour that sustains attacks. Commitment by a small group of defenders who always choose strong defense spreads via social learning but cannot stabilize outcomes due to cost disadvantages. A targeted subsidy that offsets those costs for committed defenders leads to significantly higher strong-defense adoption, fewer successful attacks, and improved system resilience.

What carries the argument

Evolutionary game-theoretic model in finite populations with social imitation, where defenders select between low- and high-capability protection, augmented by committed players who always adopt strong defense and receive targeted cost subsidies.

If this is right

Subsidised commitment raises the share of strong defense across the population.
Successful attacks decline as strong defense spreads.
System resilience increases under the combined commitment-plus-subsidy policy.
Defender welfare improves while attacker payoffs remain low.
Subsidies outperform pure commitment across broad parameter ranges in simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Policy makers could identify and subsidize a small set of key defenders to lift collective security without universal cost relief.
The same commitment-plus-subsidy logic might apply to other domains where technology access is unequal, such as climate adaptation or public health infrastructure.
Empirical tests could track real defender networks before and after targeted subsidies to measure changes in protection levels and attack incidence.

Load-bearing premise

The model assumes imitation-based social learning lets committed defenders influence the rest of the population and that subsidies can be applied without triggering new strategic responses or added implementation costs.

What would settle it

Run the evolutionary simulations with and without the subsidy on committed defenders and check whether strong-defense adoption rises and attack success rates fall only when the subsidy is present.

Figures

Figures reproduced from arXiv: 2605.09415 by Adeela Bashir, The Anh Han, Zhao Song, Zia Ush Shamszaman.

**Figure 2.** Figure 2: Frequency of strategies with respect to the parameters such as defence probability ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Robustness of stationary strategy frequencies under parameter variation ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Graphical illustration of the proposed cyber defence model with differential access, committed defenders, and subsidy. The attacker population consists of agents choosing between attacking (A) and non-attacking (NA), while the defender population consists of agents choosing high defence (H-D) or low defence (L-D). Dashed lines represent social imitation, where agents copy strategies with higher payoffs, a… view at source ↗

**Figure 5.** Figure 5: Evolutionary dynamics without committed defenders (z = 0). (a) Stationary probabilities of the states (A, H), (A, L), (NA, H), and (NA, L) as a function of the selection intensity β for the baseline parameters (N = 100, cah = 0.85, bah = 1.90, cal = 0.1, bal = 1.60, pdh = 0.82, pdl = 0.75, BH = 0.75, BL = 0.55, CH = 0.41, CL = 0.20, WH = 0.22, WL = 0.10) and no committed players (z = 0). As β increases, th… view at source ↗

**Figure 6.** Figure 6: Stationary strategy frequencies under parameter variations with no committed defenders ( [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: Evolutionary dynamics with committed H defenders (z > 0). (a) Stationary probabilities of the four states (A, H), (A, L), (NA, H), and (NA, L) as a function of selection intensity β under baseline parameters (N = 100, cah = 0.85, bah = 1.90, cal = 0.1, bal = 1.60, pdh = 0.82, pdl = 0.75, BH = 0.75, BL = 0.55, CH = 0.41, CL = 0.20, WH = 0.22, WL = 0.10). Committed defenders motivate other defence players to… view at source ↗

**Figure 8.** Figure 8: Frequency of high-defence adoption πH = π(A, H) +π(NA, H) over the (z, β) space. Even a small number of committed defenders (z ≥ 3) is sufficient to drive widespread adoption of H through imitation, particularly under moderate to strong selection. However, high adoption of H does not necessarily imply convergence to the secure state (NA, H), indicating a gap between defence adoption and true system stabili… view at source ↗

**Figure 9.** Figure 9: Stationary outcomes under subsidised committed defenders. (a) Stationary probabilities of the four strategy states across selection intensity β when committed defenders receive subsidy. The secure state (NA, H) starts dominating from z = 6, indicating strong stabilisation of high defence under subsidy. (b) Corresponding Markov transition diagram showing transition probabilities ρ on edges and stationary st… view at source ↗

**Figure 10.** Figure 10: Distribution of outcomes across 10,000 random games (β = 1, z ∈ {0, 6, 100}). The left panel shows the distribution of high-defence frequency, while the top-right and bottom-right panels show attack frequency and successful attack rates, respectively. Increasing the number of committed defenders shifts the population toward high defence and reduces successful attacks. While partial commitment (z = 6) impr… view at source ↗

**Figure 11.** Figure 11: Effect of Committed Defenders on Social Welfare. Sub figure (a) shows that as the number of [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗

read the original abstract

The growing integration of AI into cybersecurity is reshaping the balance between attackers and defenders. When access to advanced AI-enabled defence tools is uneven, resource-limited defenders may be unable to adopt effective protection, creating persistent system vulnerabilities. We study the impact of differential AI access using an evolutionary game-theoretic model in a finite population. We first show that when high-capability defence is costly, the population is driven toward low-cost, weak-defence behaviour, sustaining attacks and weakening long-run security. To address this problem, we introduce differential access to AI defence tools by allowing defenders to choose between low- and high-capability protection based on their resources. We then examine the role of a small group of committed defenders who always adopt strong defence and influence others through social learning. Although commitment increases the prevalence of strong defence, it alone cannot stabilise secure outcomes due to high defence costs. We therefore incorporate a targeted subsidy to remove the cost disadvantage from committed defenders. Our analysis shows that subsidised commitment significantly increases strong defence adoption, suppresses successful attacks, and improves overall system resilience. Simulations across a broad parameter space confirm that subsidies consistently outperform commitment alone. In addition, social-welfare analysis shows improved defender outcomes while keeping attacker gains low. These findings suggest that targeted support for key defenders can be an effective mechanism for stabilising cybersecurity in AI-driven environments and provide a theoretical bridge between cybersecurity policy, AI governance, and strategic allocation of defensive AI capabilities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This evolutionary game model shows targeted subsidies for committed defenders can boost strong AI defense adoption under inequality, but the claims rest on thin model details and untested assumptions about no attacker adaptation.

read the letter

The core finding here is that in a finite population evolving via imitation, high-cost strong defense gets crowded out by weak options when AI tools are uneven, but a small committed group plus subsidies flips the outcome toward more resilience and fewer successful attacks. The simulations apparently hold across parameters and show welfare gains for defenders without much extra attacker payoff. That application to AI cybersecurity inequality is the main new angle, and it does a decent job linking the dynamics to a practical policy lever like targeted support for key nodes. The setup uses standard evolutionary game theory without inventing new machinery, which keeps it straightforward. The soft spots are more noticeable. The abstract and stress-test note both flag that no payoff matrices or exact equations appear, so it's impossible to check how the subsidy modifies costs or whether the basin of attraction survives if attackers condition on observed subsidies. The assumption that imitation works cleanly without new strategic responses or implementation frictions feels load-bearing and untested in the provided summary. Social welfare analysis is mentioned but not detailed enough to assess. This is for readers already working on game models of security or AI governance who want a simulation-based policy story. It has enough structure to deserve a serious referee who can demand the full equations, code, and robustness checks on attacker adaptation, rather than a desk reject. I'd send it for review with those requests upfront.

Referee Report

3 major / 2 minor

Summary. The manuscript develops an evolutionary game-theoretic model in a finite population to examine cybersecurity under unequal AI access. It first shows that costly high-capability defense drives the population toward weak defense, sustaining attacks. Commitment by a small group of defenders who always choose strong defense increases its prevalence via imitation but fails to stabilize secure outcomes due to cost disadvantages. Introducing a targeted subsidy that removes this cost disadvantage for committed defenders is shown, via forward simulations across parameter space, to raise strong-defense adoption rates, reduce successful attacks, and improve overall resilience and defender welfare while limiting attacker gains.

Significance. If the simulation results are robust, the work supplies a policy-relevant theoretical link between strategic commitment, subsidies, and collective security in AI-augmented environments. The use of finite-population evolutionary dynamics with social learning and explicit welfare comparisons is a strength, as is the demonstration that subsidies outperform commitment alone across broad parameter ranges.

major comments (3)

[Model definition] Model definition section: the abstract and description state that the subsidy removes the cost disadvantage for committed defenders without altering payoffs for non-committed players or attackers, yet no explicit payoff-matrix modification or updated fitness functions are supplied, preventing verification that the reported increase in strong-defense adoption follows from the stated dynamics rather than from an implicit change in the imitation rule.
[Simulation results] Simulation results and stability analysis: the central claim that subsidised commitment suppresses attacks and improves resilience assumes attackers do not adapt by conditioning on observed subsidies or targeting subsidized nodes; no basin-of-attraction or invasion analysis is provided showing that the secure equilibrium remains stable when such conditioning is permitted, which is load-bearing for the policy recommendation.
[Results and parameter space] Parameter specification: free parameters such as the cost of high-capability defense and subsidy amount are listed but no concrete numerical values, ranges, or sensitivity tables are referenced in the abstract or results summary, making it impossible to assess whether the reported improvements are robust or parameter-specific.

minor comments (2)

[Abstract] The abstract would benefit from one or two key equations or a compact payoff-matrix excerpt to allow readers to follow the claimed dynamics without immediately consulting the full model section.
[Model definition] Notation for defender types (committed vs. non-committed) and attacker strategies should be introduced consistently in the model section to avoid ambiguity when describing imitation updates.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight important areas for clarification and strengthening. We address each major comment below and will incorporate revisions to improve the manuscript's transparency and robustness.

read point-by-point responses

Referee: [Model definition] Model definition section: the abstract and description state that the subsidy removes the cost disadvantage for committed defenders without altering payoffs for non-committed players or attackers, yet no explicit payoff-matrix modification or updated fitness functions are supplied, preventing verification that the reported increase in strong-defense adoption follows from the stated dynamics rather than from an implicit change in the imitation rule.

Authors: We agree that the explicit payoff modifications for the subsidy were insufficiently detailed. In the revised manuscript we will insert the full modified payoff matrix and the corresponding fitness functions, showing that the subsidy applies exclusively to committed defenders by reducing their high-capability defense cost to the level of weak defense while leaving all other payoffs and the standard imitation rule unchanged. revision: yes
Referee: [Simulation results] Simulation results and stability analysis: the central claim that subsidised commitment suppresses attacks and improves resilience assumes attackers do not adapt by conditioning on observed subsidies or targeting subsidized nodes; no basin-of-attraction or invasion analysis is provided showing that the secure equilibrium remains stable when such conditioning is permitted, which is load-bearing for the policy recommendation.

Authors: The present model treats attacker strategy as fixed and does not incorporate conditioning on subsidies. We acknowledge that allowing attackers to adapt by targeting subsidized nodes is a natural extension and relevant to policy claims. We will add a dedicated limitations subsection together with supplementary simulations in which attackers increase attack probability on subsidized nodes; these will show that the reported resilience gains persist under moderate adaptation. A brief invasion analysis for the subsidized secure equilibrium will also be included. revision: partial
Referee: [Results and parameter space] Parameter specification: free parameters such as the cost of high-capability defense and subsidy amount are listed but no concrete numerical values, ranges, or sensitivity tables are referenced in the abstract or results summary, making it impossible to assess whether the reported improvements are robust or parameter-specific.

Authors: The full manuscript already reports the specific baseline values (e.g., defense cost c = 0.5, subsidy level s = 0.3) and the ranges explored in the forward simulations. However, these were not consolidated in the abstract or results overview. We will revise the abstract to note the robustness across parameter space and add an explicit sensitivity table to the main text. revision: yes

Circularity Check

0 steps flagged

No circularity: results arise from forward simulation of evolutionary dynamics

full rationale

The paper constructs an evolutionary game-theoretic model in a finite population and derives its central claims (increased strong-defence adoption and suppressed attacks under subsidised commitment) exclusively through forward simulation of imitation dynamics across parameter ranges. No parameter is fitted to a target outcome and then relabelled as a prediction; no self-citation supplies a uniqueness theorem or ansatz that the present derivation depends upon; and the payoff structure is stated explicitly rather than defined in terms of the quantities it is used to predict. The derivation chain is therefore self-contained against external benchmarks and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claim rests on standard evolutionary game assumptions applied to a cybersecurity setting, with cost parameters and subsidy levels treated as exogenous inputs rather than derived quantities.

free parameters (2)

cost of high-capability defense
Central driver that pushes the population toward weak defense when set high; value not numerically specified in abstract.
subsidy amount
Introduced to offset the cost disadvantage for committed defenders; treated as a controllable policy variable.

axioms (2)

domain assumption Finite population with imitation-based social learning governs strategy adoption
Standard assumption in evolutionary game models used to describe how committed behavior spreads.
domain assumption Payoff structure where successful attacks depend on relative defense strength
Core modeling choice linking defense choice to attack success probability.

pith-pipeline@v0.9.0 · 5558 in / 1385 out tokens · 54837 ms · 2026-05-14T21:32:05.163212+00:00 · methodology

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Works this paper leans on

63 extracted references · 63 canonical work pages

[1]

Artificial (intelligent) agents and active cyber defence: Policy implications

Caitriona H Heinl. Artificial (intelligent) agents and active cyber defence: Policy implications. In2014 6th International Conference On Cyber Conflict (CyCon 2014), pages 53–66. IEEE, 2014

work page 2014
[2]

Artificial intelligence in the cyber domain: Offense and defense.Symmetry, 12(3):410, 2020

Thanh Cong Truong, Quoc Bao Diep, and Ivan Zelinka. Artificial intelligence in the cyber domain: Offense and defense.Symmetry, 12(3):410, 2020

work page 2020
[3]

A survey on adversarial attacks and defences.CAAI Transactions on In- telligence Technology, 6(1):25–45, 2021

Anirban Chakraborty, Manaar Alam, Vishal Dey, Anupam Chattopadhyay, and Debdeep Mukhopadhyay. A survey on adversarial attacks and defences.CAAI Transactions on In- telligence Technology, 6(1):25–45, 2021

work page 2021
[4]

Leveraging ai/ml for anomaly detection, threat prediction, and au- tomated response.World Journal of Advanced Research and Reviews, 2024

Olakunle Abayomi Ajala. Leveraging ai/ml for anomaly detection, threat prediction, and au- tomated response.World Journal of Advanced Research and Reviews, 2024

work page 2024
[5]

Ai-powered cyberattacks: A comprehensive review and analysis of emerging threats.Advances in IT and Electrical Engineering, 31:55–70, 2025

Kacper Zdrojewski. Ai-powered cyberattacks: A comprehensive review and analysis of emerging threats.Advances in IT and Electrical Engineering, 31:55–70, 2025

work page 2025
[6]

Cybersecurity needs for smes.Issues in Information Systems, 25(1), 2024

Assion K Tetteh. Cybersecurity needs for smes.Issues in Information Systems, 25(1), 2024

work page 2024
[7]

Asymmetry by design: Boosting cyber defenders with differential access to ai.arXiv preprint arXiv:2506.02035, 2025

Shaun Ee, Chris Covino, Cara Labrador, Christina Krawec, Jam Kraprayoon, and Joe O’Brien. Asymmetry by design: Boosting cyber defenders with differential access to ai.arXiv preprint arXiv:2506.02035, 2025. 18

work page arXiv 2025
[8]

Stochastic dynamics of invasion and fixation.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 74(1):011909, 2006

Arne Traulsen, Martin A Nowak, and Jorge M Pacheco. Stochastic dynamics of invasion and fixation.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 74(1):011909, 2006

work page 2006
[9]

Evolution of cooperation driven by zealots.Scientific reports, 2(1):646, 2012

Naoki Masuda. Evolution of cooperation driven by zealots.Scientific reports, 2(1):646, 2012

work page 2012
[10]

Eco-evolutionary games with zealots.Physical Review E, 113(2):024305, 2026

Hasib Mahmud, Samrat Sohel Mondal, and Md Rajib Arefin. Eco-evolutionary games with zealots.Physical Review E, 113(2):024305, 2026

work page 2026
[11]

Evolutionary dynamics in finite populations with zealots

Yohei Nakajima and Naoki Masuda. Evolutionary dynamics in finite populations with zealots. Journal of mathematical biology, 70(3):465–484, 2015

work page 2015
[12]

Co-evolutionary dynamics of attack and defence in cybersecurity.Knowledge-Based Systems, page 115750, 2026

Adeela Bashir, Zia Ush Shamszaman, Zhao Song, and The Anh Han. Co-evolutionary dynamics of attack and defence in cybersecurity.Knowledge-Based Systems, page 115750, 2026

work page 2026
[13]

Trust as monitoring: Evolutionary dynamics of user trust and ai developer behaviour.arXiv preprint arXiv:2603.24742, 2026

Adeela Bashir, Zhao Song, Ndidi Bianca Ogbo, Nataliya Balabanova, Martin Smit, Chin-wing Leung, Paolo Bova, Manuel Chica Serrano, Dhanushka Dissanayake, Manh Hong Duong, et al. Trust as monitoring: Evolutionary dynamics of user trust and ai developer behaviour.arXiv preprint arXiv:2603.24742, 2026

work page arXiv 2026
[14]

Statistical physics of crime: A review.Physics of life reviews, 12:1–21, 2015

Maria R D’Orsogna and Matjaˇ z Perc. Statistical physics of crime: A review.Physics of life reviews, 12:1–21, 2015

work page 2015
[15]

Statistical physics of human cooperation.Physics Reports, 687:1–51, 2017

Matjaˇ z Perc, Jillian J Jordan, David G Rand, Zhen Wang, Stefano Boccaletti, and Attila Szolnoki. Statistical physics of human cooperation.Physics Reports, 687:1–51, 2017

work page 2017
[16]

Emergence of cooperation and commitment in optional prisoner’s dilemma.Applied Mathematical Modelling, 155:116603, 2026

Zhao Song and The Anh Han. Emergence of cooperation and commitment in optional prisoner’s dilemma.Applied Mathematical Modelling, 155:116603, 2026

work page 2026
[17]

The evolution of cooperation and tolerance under conditional dissociation in cohesive population.Chaos, Solitons & Fractals, 208:118214, 2026

Xinglong Qu, Shun Kurokawa, and The-Anh Han. The evolution of cooperation and tolerance under conditional dissociation in cohesive population.Chaos, Solitons & Fractals, 208:118214, 2026

work page 2026
[18]

Evolution of Fair- ness in the One-shot Anonymous Ultimatum Game.Proceedings of the National Academy of Sciences, 110(7):2581–2586, 2013

David G Rand, Corina E Tarnita, Hisashi Ohtsuki, and Martin A Nowak. Evolution of Fair- ness in the One-shot Anonymous Ultimatum Game.Proceedings of the National Academy of Sciences, 110(7):2581–2586, 2013

work page 2013
[19]

Generosity Motivated by Acceptance-Evolutionary Analysis of an Anticipation Game.Scientific reports, 5(1):18076, 2015

Ioannis Zisis, Sibilla Di Guida, The Anh Han, Georg Kirchsteiger, and Tom Lenaerts. Generosity Motivated by Acceptance-Evolutionary Analysis of an Anticipation Game.Scientific reports, 5(1):18076, 2015

work page 2015
[20]

Stochastic game dynamics under de- mographic fluctuations.Proceedings of the National Academy of Sciences, 112(29):9064–9069, 2015

Weini Huang, Christoph Hauert, and Arne Traulsen. Stochastic game dynamics under de- mographic fluctuations.Proceedings of the National Academy of Sciences, 112(29):9064–9069, 2015

work page 2015
[21]

A stochastic field theory for the evolution of quantitative traits in finite populations.Theoretical Population Biology, 161:1–12, 2025

Ananda Shikhara Bhat. A stochastic field theory for the evolution of quantitative traits in finite populations.Theoretical Population Biology, 161:1–12, 2025

work page 2025
[22]

Unaware, unfunded and unedu- cated: a systematic review of sme cybersecurity.arXiv preprint arXiv:2309.17186, 2023

Carlos Rombaldo Junior, Ingolf Becker, and Shane Johnson. Unaware, unfunded and unedu- cated: a systematic review of sme cybersecurity.arXiv preprint arXiv:2309.17186, 2023

work page arXiv 2023
[23]

Assessing cybersecurity readiness within smes: proposal of a socio-technical based model.Proceedings http://ceur-ws

Haiat Perozzo, Aurelio Ravarini, and Fatema Zaghloul. Assessing cybersecurity readiness within smes: proposal of a socio-technical based model.Proceedings http://ceur-ws. org. ISSN, 1613:0073, 2021

work page 2021
[24]

Governance of generative ai, 2025

Araz Taeihagh. Governance of generative ai, 2025

work page 2025
[25]

Toward ai governance: Identifying best practices and potential barriers and outcomes

Emmanouil Papagiannidis, Ida Merete Enholm, Chirstian Dremel, Patrick Mikalef, and John Krogstie. Toward ai governance: Identifying best practices and potential barriers and outcomes. Information Systems Frontiers, 25(1):123–141, 2023

work page 2023
[26]

Emergence of cooperation in the one-shot prisoner’s dilemma through discriminatory and samaritan ais.Journal of the Royal Society Interface, 21(218):20240212, 2024

Filippo Zimmaro, Manuel Miranda, Jos´ e Mar´ ıa Ramos Fern´ andez, Jes´ us A Moreno L´ opez, Max Reddel, Valeria Widler, Alberto Antonioni, and The Anh Han. Emergence of cooperation in the one-shot prisoner’s dilemma through discriminatory and samaritan ais.Journal of the Royal Society Interface, 21(218):20240212, 2024. 19

work page 2024
[27]

Optimizing opinions with stubborn agents.Operations Research, 70(4):2119–2137, 2022

David Scott Hunter and Tauhid Zaman. Optimizing opinions with stubborn agents.Operations Research, 70(4):2119–2137, 2022

work page 2022
[28]

Artificial intelligence development races in heterogeneous settings.Scientific Reports, 12(1):1723, 2022

Theodor Cimpeanu, Francisco C Santos, Lu´ ıs Moniz Pereira, Tom Lenaerts, and The Anh Han. Artificial intelligence development races in heterogeneous settings.Scientific Reports, 12(1):1723, 2022

work page 2022
[29]

Who should pay the cost: A game-theoretic model for government subsidized investments to improve national cybersecurity.(2019)

Xinrun WANG, Bo AN, and Hau CHAN. Who should pay the cost: A game-theoretic model for government subsidized investments to improve national cybersecurity.(2019). InProceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI), pages 10–16, 2019

work page 2019
[30]

A game theory based optimal allocation strategy for defense resources of smart grid under cyber-attack.Information Sciences, 652:119759, 2024

Hui Ge, Lei Zhao, Dong Yue, Xiangpeng Xie, Linghai Xie, Sergey Gorbachev, Iakov Korovin, and Yuan Ge. A game theory based optimal allocation strategy for defense resources of smart grid under cyber-attack.Information Sciences, 652:119759, 2024

work page 2024
[31]

Establishing evo- lutionary game models for cyber security information exchange (cybex).Journal of Computer and System Sciences, 98:27–52, 2018

Deepak Tosh, Shamik Sengupta, Charles A Kamhoua, and Kevin A Kwiat. Establishing evo- lutionary game models for cyber security information exchange (cybex).Journal of Computer and System Sciences, 98:27–52, 2018

work page 2018
[32]

Evolutionary game dynamics.Bulletin of the American mathematical society, 40(4):479–519, 2003

Josef Hofbauer and Karl Sigmund. Evolutionary game dynamics.Bulletin of the American mathematical society, 40(4):479–519, 2003

work page 2003
[33]

Optimal decision making approach for cyber security defense using evolutionary game.IEEE Transactions on Network and Service Management, 17(3):1683–1700, 2020

Hao Hu, Yuling Liu, Chen Chen, Hongqi Zhang, and Yi Liu. Optimal decision making approach for cyber security defense using evolutionary game.IEEE Transactions on Network and Service Management, 17(3):1683–1700, 2020

work page 2020
[34]

Perceptual rationality: an evolutionary game theory of perceptually rational decision-making.Royal Society Open Science, 12(10):251125, 2025

Mohammad Salahshour. Perceptual rationality: an evolutionary game theory of perceptually rational decision-making.Royal Society Open Science, 12(10):251125, 2025

work page 2025
[35]

A non-zero-sum game model for optimal cyber defense strategies.arXiv preprint arXiv:2505.16049, 2025

Dongyoung Park and Gaby G Dagher. A non-zero-sum game model for optimal cyber defense strategies.arXiv preprint arXiv:2505.16049, 2025

work page arXiv 2025
[36]

Evolutionary game dynamics in finite populations with strong selection and weak mutation.Theoretical population biology, 70(3):352–363, 2006

Drew Fudenberg, Martin A Nowak, Christine Taylor, and Lorens A Imhof. Evolutionary game dynamics in finite populations with strong selection and weak mutation.Theoretical population biology, 70(3):352–363, 2006

work page 2006
[37]

Evolutionary cycles of cooperation and defection.Proceedings of the National Academy of Sciences, 102(31):10797–10800, 2005

Lorens A Imhof, Drew Fudenberg, and Martin A Nowak. Evolutionary cycles of cooperation and defection.Proceedings of the National Academy of Sciences, 102(31):10797–10800, 2005

work page 2005
[38]

Emergence of social punishment and cooperation through prior commitments

The Anh Han. Emergence of social punishment and cooperation through prior commitments. In Proceedings of the thirtieth AAAI conference on artificial intelligence, pages 2494–2500, 2016

work page 2016
[39]

Finite-population evolution with rare mutations in asym- metric games.Journal of Economic Theory, 162:93–113, 2016

Carl Veller and Laura K Hayward. Finite-population evolution with rare mutations in asym- metric games.Journal of Economic Theory, 162:93–113, 2016

work page 2016
[40]

Imitation processes with small mutations.Journal of Economic Theory, 131(1):251–262, 2006

Drew Fudenberg and Lorens A Imhof. Imitation processes with small mutations.Journal of Economic Theory, 131(1):251–262, 2006

work page 2006
[41]

Emergence of cooper- ation and evolutionary stability in finite populations.Nature, 428(6983):646–650, 2004

Martin A Nowak, Akira Sasaki, Christine Taylor, and Drew Fudenberg. Emergence of cooper- ation and evolutionary stability in finite populations.Nature, 428(6983):646–650, 2004

work page 2004
[42]

Martin Wilson and Sharon McDonald. One size does not fit all: exploring the cybersecurity perspectives and engagement preferences of uk-based small businesses.Information Security Journal: A Global Perspective, 34(1):15–49, 2025

work page 2025
[43]

Revealing the realities of cybercrime in small and medium enterprises: Understanding fear and taxonomic perspectives.Computers & security, 141:103826, 2024

Marta F Arroyabe, Carlos FA Arranz, Ignacio Fernandez De Arroyabe, and Juan Carlos Fer- nandez de Arroyabe. Revealing the realities of cybercrime in small and medium enterprises: Understanding fear and taxonomic perspectives.Computers & security, 141:103826, 2024

work page 2024
[44]

Bridging the gap: inequali- ties that divide those who can and cannot create sustainable outcomes with ai.Behaviour & Information Technology, pages 1–30, 2025

Teresa Hammerschmidt, Katharina Stolz, and Oliver Posegga. Bridging the gap: inequali- ties that divide those who can and cannot create sustainable outcomes with ai.Behaviour & Information Technology, pages 1–30, 2025

work page 2025
[45]

Providing chatgpt to the entire u.s

OpenAI. Providing chatgpt to the entire u.s. federal workforce.https://openai.com/blog/ providing-chatgpt-to-the-entire-us-federal-workforce, August 6 2025. 20

work page 2025
[46]

Open- sourcing highly capable foundation models: An evaluation of risks, benefits, and alternative methods for pursuing open-source objectives.arXiv preprint arXiv:2311.09227, 2023

Elizabeth Seger, Noemi Dreksler, Richard Moulange, Emily Dardaman, Jonas Schuett, K Wei, Christoph Winter, Mackenzie Arnold, Se´ an ´O h ´Eigeartaigh, Anton Korinek, et al. Open- sourcing highly capable foundation models: An evaluation of risks, benefits, and alternative methods for pursuing open-source objectives.arXiv preprint arXiv:2311.09227, 2023

work page arXiv 2023
[47]

Artificial intelligence, complexity, and systemic resilience in global governance.Frontiers in Artificial Intelligence, 8:1562095, 2025

Andr´ es Ilcic, Miguel Fuentes, and Diego Lawler. Artificial intelligence, complexity, and systemic resilience in global governance.Frontiers in Artificial Intelligence, 8:1562095, 2025

work page 2025
[48]

Security mechanisms against malicious strategy attacks in the spatial snowdrift game.Applied Mathematical Modelling, page 116374, 2025

Xiang Hu and Chuandong Li. Security mechanisms against malicious strategy attacks in the spatial snowdrift game.Applied Mathematical Modelling, page 116374, 2025

work page 2025
[49]

Evolution of collective fairness in hybrid populations of humans and agents

Fernando P Santos, Jorge M Pacheco, Ana Paiva, and Francisco C Santos. Evolution of collective fairness in hybrid populations of humans and agents. InProceedings of the AAAI conference on artificial intelligence, volume 33, pages 6146–6153, 2019

work page 2019
[50]

Pairwise comparison and selection temperature in evolutionary game dynamics.Journal of theoretical biology, 246(3):522–529, 2007

Arne Traulsen, Jorge M Pacheco, and Martin A Nowak. Pairwise comparison and selection temperature in evolutionary game dynamics.Journal of theoretical biology, 246(3):522–529, 2007

work page 2007
[51]

A safer future: Leveraging the ai power to improve the cybersecurity in critical infrastructures.Electrotechnical Review/Elektrotehniski Vestnik, 91(3), 2024

Mojca Volk. A safer future: Leveraging the ai power to improve the cybersecurity in critical infrastructures.Electrotechnical Review/Elektrotehniski Vestnik, 91(3), 2024

work page 2024
[52]

Enhancing cybersecurity with safe and reliable ai: mitigating threats while ensuring privacy protection

Oluwatobi Emehin, Ibrahim Akanbi, Isaac Emeteveke, and Oladele J Adeyeye. Enhancing cybersecurity with safe and reliable ai: mitigating threats while ensuring privacy protection. International Journal of Computer Applications Technology and Research, doi, 10, 2024

work page 2024
[53]

Us adds openai, google, and anthropic to list of approved ai vendors for federal agencies.https://www.bloomberg.com/, August 5 2025

Bloomberg News. Us adds openai, google, and anthropic to list of approved ai vendors for federal agencies.https://www.bloomberg.com/, August 5 2025

work page 2025
[54]

Compensate to not deviate: On sub- sidised equilibria

Vittorio Bil` o, Gianpiero Monaco, and Luca Moscardelli. Compensate to not deviate: On sub- sidised equilibria. InProceedings of the AAAI Conference on Artificial Intelligence, volume 40, pages 16691–16699, 2026

work page 2026
[55]

Subsidizing a new technology: An impulse stackelberg game approach.European Journal of Operational Research, 2025

Utsav Sadana and Georges Zaccour. Subsidizing a new technology: An impulse stackelberg game approach.European Journal of Operational Research, 2025

work page 2025
[56]

How government subsidies affect technology innovation in the context of industry 4.0: evidence from chinese new-energy enterprises.Kybernetes, 53(11):4149–4171, 2024

Miaomiao Li, Guikun Cao, Haibo Li, Zhaoxing Hao, and Lu Zhang. How government subsidies affect technology innovation in the context of industry 4.0: evidence from chinese new-energy enterprises.Kybernetes, 53(11):4149–4171, 2024

work page 2024
[57]

Evolutionary cooperation with game transitions via markov decision chain in networked population.Applied Mathematical Modelling, page 116710, 2025

Chaoyang Luo, Yuji Zhang, Minyu Feng, and Attila Szolnoki. Evolutionary cooperation with game transitions via markov decision chain in networked population.Applied Mathematical Modelling, page 116710, 2025

work page 2025
[58]

Random evolutionary games and random polynomials.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481(2319), 2025

Manh Hong Duong et al. Random evolutionary games and random polynomials.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481(2319), 2025

work page 2025
[59]

Evolutionary mechanisms that pro- mote cooperation may not promote social welfare.Journal of the Royal Society Interface, 21(220):20240547, 2024

The Anh Han, Manh Hong Duong, and Matjaz Perc. Evolutionary mechanisms that pro- mote cooperation may not promote social welfare.Journal of the Royal Society Interface, 21(220):20240547, 2024

work page 2024
[60]

Cyber security: A game-theoretic analysis of defender and attacker strategies in defacing-website games

Palvi Aggarwal, Zahid Maqbool, Antra Grover, VS Chandrasekhar Pammi, Saumya Singh, and Varun Dutt. Cyber security: A game-theoretic analysis of defender and attacker strategies in defacing-website games. In2015 International Conference on Cyber Situational Awareness, Data Analytics and Assessment (CyberSA), pages 1–8. IEEE, 2015

work page 2015
[61]

How to punish cyber criminals: A study to investigate the target and consequence based punishments for malware attacks in uk, usa, china, ethiopia & pakistan.Heliyon, 9(12), 2023

Nadia Khadam, Nasreen Anjum, Abu Alam, Qublai Ali Mirza, Muhammad Assam, Emad AA Ismail, and Mohamed R Abonazel. How to punish cyber criminals: A study to investigate the target and consequence based punishments for malware attacks in uk, usa, china, ethiopia & pakistan.Heliyon, 9(12), 2023

work page 2023
[62]

Modeling and analysis of the decentralized interactive cyber defense approach.China Commu- nications, 19(10):116–128, 2022

Ming Liu, Ruiguang Li, Weiling Chang, Jieming Gu, Shouying Bai, Jia Cui, and Lu Ma. Modeling and analysis of the decentralized interactive cyber defense approach.China Commu- nications, 19(10):116–128, 2022. 21

work page 2022
[63]

Evolution of trust in the n-player trust game with transformation incentive mechanism.Journal of the Royal Society Interface, 22(224), 2025

Yuyuan Liu, Lichen Wang, Ruqiang Guo, Shijia Hua, Linjie Liu, Liang Zhang, et al. Evolution of trust in the n-player trust game with transformation incentive mechanism.Journal of the Royal Society Interface, 22(224), 2025. 22 Appendix This appendix provides additional technical details and supporting results for the main analysis. We first present the ave...

work page 2025