Dynamic Outcome Distributions Under Strategic Uncertainty

The preceding papers in this series established the conceptual framework for Distributed Resilience Doctrine (WP-02), the Strategic Termination Time metric (WP-03), C2-CI formalisation (WP-04), operationalisation toolkit (WP-05), and the nonlinear dynamics of C2 degradation including bifurcation and hysteresis (WP-06). What has been absent is a quantitative outcome distribution across competing posture scenarios under realistic uncertainty.

Two developments make this analysis timely. First, the fiscal trajectory has hardened: the 5th-generation multirole aircraft programme represents a lifecycle commitment of approximately €25–30 billion, constraining the defence budget for decades in ways that were not fully priced into the original acquisition decision. Second, the threat environment has evolved: the adversary's standoff precision munition production reached approximately 12,000 units annually by late 2025, with monthly employment rates exceeding 180 per day in the Ukrainian theatre. The standoff precision strike aircraft's operational pattern — releasing FAB-500/1500 glide munitions from 70–100 km standoff, outside the engagement envelope of most ground-based air defence — represents a structural challenge for which platform-centric posture offers no direct response.

This paper does not advocate policy. It quantifies outcome distributions under specified assumptions, making the strategic trade-offs visible in probabilistic terms.

2.1 Five-Phase Sequential Structure

The simulation proceeds through five conditional phases. Each phase draws from specified probability distributions; outcomes of earlier phases condition the distributions of later phases.

2.2 Variable Distributions

2.3 Terminal Outcome Categories

• Strategic success — sovereignty maintained, conflict terminated without territorial loss
• Protracted attrition — no rapid outcome, allied intervention window opens (DRD objective)
• Rapid strategic defeat — the adversaryn objectives achieved within 14 days
• Fiscal collapse — economic attrition forces capitulation before military decision

Scenario A: Platform-Centric (64 5th-generation multirole aircraft, limited GBAD)

Scenario B: DRD-Optimal (32–40 5th-generation multirole aircraft, distributed GBAD, infrastructure resilience)

Scenario C: Current Compromise (64 5th-generation multirole aircraft, partial GBAD, no systemic resilience)

The most consequential single variable is US commitment level. Platform-centric posture is structurally dependent on high US commitment (p≈0.20). DRD is robust across all commitment levels.

Platform-Centric (Scenario A)

DRD-Optimal (Scenario B)

DRD's robustness to US commitment variation is its most strategically significant property. In an era of documented NATO credibility stress — including public questioning of collective defence obligation by executive authority — a posture that performs adequately without US intervention represents a fundamentally different risk profile than one that collapses at low commitment levels.

Varying one factor at a time against the DRD baseline identifies which variables most significantly affect outcomes.

The standoff precision strike aircraft result is structurally important: it validates the central technical argument of WP-02. The platform-centric model has no direct answer to standoff standoff precision munition employment — 5th-generation multirole aircraft sorties require operating airspace that standoff precision munition raids do not. The solution space is long-range GBAD (150+ km engagement envelope) or forward-based dispersed fighters operating from road strips without centralised C2 dependency. Neither is currently fielded at adequate scale.

Full DRD transition is fiscally foreclosed. The 5th-generation multirole aircraft programme represents a sunk cost in the decision-theoretic sense: the acquisition is complete, and the lifecycle commitment is politically and contractually irreversible within the current planning cycle. Relitigating the acquisition decision is not analytically productive.

What remains is the identification of compensatory measures that improve outcome distributions within the existing fiscal envelope. Three categories are available.

First: 5th-generation multirole aircraft integration into NATO ISR chain. The platform's most significant underexploited capability is its sensor fusion and data-link architecture. Integrated into NATO's airborne early warning platform and ground-based sensor network, 5th-generation multirole aircraft can serve as a C2 node and targeting relay for ground-based systems it cannot directly engage. This requires investment in interoperability infrastructure rather than additional platforms.

Second: Dispersed basing and road strip capability. The most immediate DRD-compatible measure is pre-positioning fuel, ordnance, and maintenance capability at dispersed civilian airfield locations. This reduces the high-value target density at primary bases and extends the operational window before C2 degradation reaches bifurcation threshold (WP-06). Investment cost is modest relative to platform cost.

Third: Infrastructure resilience as force multiplier. Finnish energy infrastructure resilience — the subject of the parallel ACI SGFA analysis — directly affects C2-CI. Distributed energy nodes that can sustain C2 function independent of grid connectivity reduce the effectiveness of infrastructure-targeted strikes in the hybrid phase. This is the structural connection between the DRD series and the SGFA investment programme: resilient energy infrastructure is not civilian policy — it is defence-relevant C2 sustainment.

The fiscal endurance parameter (Normal μ=4, σ=1.5 months) is the least empirically grounded variable in the model. A historical reference case provides partial validation: the 2009–2018 debt crisis of a southern European eurozone member state demonstrates the mechanics of fiscal attrition under external pressure without military conflict.

The case trajectory follows the bifurcation pattern described in WP-06 with precision. The state did not collapse suddenly — it drifted toward the critical threshold over five years of slow deterioration before the abrupt phase transition: GDP contracted 25%, unemployment reached 25% of the labour force, and political cohesion fractured as emergency coalition governments alternated with radical opposition movements. The system exhibited classic critical slowing down — recovery time from fiscal perturbations lengthened progressively before the crisis peak — but this signal was not measured in operational time.

Three structural observations transfer directly to small-state defence analysis.

First, the external intervention that prevented full collapse — a central bank commitment to prevent eurozone dissolution — was a non-replicable event. The mechanism depended on a specific institutional mandate that does not extend to states under hybrid or kinetic pressure. A state facing simultaneous fiscal attrition and security stress cannot assume an equivalent intervention.

Second, defence expenditure did not protect against fiscal crisis. The case state maintained defence spending above 5% of GDP through the crisis period — among the highest in the alliance — while simultaneously being forced to cut defence budgets 8% between 2010 and 2015. High platform investment and fiscal fragility coexisted, then compounded.

Third, political cohesion fractured at approximately the four-month mark of acute crisis — consistent with the μ=4 model parameter. When hospital queues formed and food distribution points appeared, the political centre could not hold. Radical formations captured government within five years of crisis onset. This is WP-02's societal resilience pillar expressed as empirical outcome: it is not a soft value but a measurable strategic variable that degrades under fiscal stress independently of military threat.

Projecting forward: defence expenditure rising to approximately 8.5 billion annually combined with debt service costs rising from 3.2 billion to an estimated 6.3 billion by 2030 produces a combined fixed obligation approaching 15 billion — a structural commitment that leaves declining room for the distributed resilience investments (energy node infrastructure, dispersed C2 capacity, infrastructure hardening) that DRD requires. The fiscal path-dependency identified earlier in this section is not hypothetical. It has a documented historical analogue in which the same dynamic — high platform investment, rising debt service, compressed resilience investment — produced exactly the outcome distribution that Scenario A projects.

The Monte Carlo analysis produces three findings that are robust across parameter variation.

First, platform-centric posture is critically fragile to US commitment variation. At low US commitment (p=0.25), rapid defeat probability reaches 68%. This is not a tail risk — it is the modal outcome under one of three plausible US posture scenarios. The platform-centric model was calibrated for a strategic environment that may not persist.

Second, DRD posture produces the protracted attrition outcome that small-state NATO strategy requires. At 48% probability across all US commitment scenarios, protracted attrition is the DRD modal outcome. This is the condition under which collective defence obligation activation has operational meaning — it provides the temporal window for allied intervention that rapid defeat forecloses.

Third, the standoff precision strike aircraft standoff precision munition problem is the single variable that most significantly degrades all scenarios. No current Finnish capability reliably suppresses standoff standoff precision munition employment. This represents the primary capability gap that compensatory investment should address — not additional strike platforms, but extended-range GBAD and dispersed C2 architecture.

the case state chose its strategy before the current threat environment was fully apparent and before the current US commitment uncertainty was measurable. The choice cannot be undone. What can be done is to maximise the DRD-compatible elements within the existing platform investment — dispersal, ISR integration, and infrastructure resilience — at the margin of the available fiscal envelope.

The analytical framework developed in this paper received independent institutional validation in April 2026, when the national supply security authority published a scenario document titled "Suomeen kohdistuva sotilaallinen voimankäyttö ja huoltovarmuus" (Military Use of Force against Finland and Supply Security). The document was prepared in cooperation with the defence forces, the cybersecurity centre, and the national regulatory authority, and released publicly for use by the entire business community after earlier restricted distribution to supply-security-critical companies.

Three passages in the institutional document directly validate the analytical premises of this paper. First: "Operational reliability takes precedence over efficiency. Instead of the cheapest option, preference is given to choices that are correctable and manageable domestically." This is the DRD posture argument stated as official policy — distributed, repairable, domestically controllable capacity is explicitly preferred over optimised but fragile centralised systems. Second: "Every disruption in infrastructure is felt at the front, and every success on the civilian side also strengthens military capability." This confirms the C2-CI linkage formalised in WP-06: civilian infrastructure resilience and military command continuity are not separable domains. Third: "Responsibility would shift increasingly to citizens, organisations, companies and local actors." This is the distributed resilience principle — the architectural preference for networked local nodes over centralised dependency — expressed as the anticipated operational reality under stress conditions.

The institutional document explicitly characterises military conflict as unlikely but serious if realised — consistent with the probability weights used in this paper's Phase 2 escalation distribution. Its publication does not change the quantitative parameters of the Monte Carlo model. It does, however, confirm that the threat structure, the infrastructure dependency, and the distributed resilience imperative that motivate this analysis are shared by the institutions responsible for national preparedness. The analysis in this paper was conducted independently and prior to the institutional document's public release. The convergence is substantive rather than coincidental: both derive from the same underlying structural conditions.

The following three analytical extensions were developed through structured adversarial modelling in May 2026, stress-testing DRD-07's core results against a hybrid A/G/R allocation framework (DAGRA: Distributed Air-Ground Resilience Architecture). They extend, rather than revise, the original simulation findings.

Extension 1 — E×D Two-Dimensional Infrastructure Resilience

DRD-07's R-layer (infrastructure resilience) was treated as a single composite variable. Adversarial modelling demonstrates that R must be decomposed into two independent dimensions:

• E (Energy Resilience Index): 0 = grid fully dark, 1 = all critical nodes islanded with backup power. λ_E = 3.0 (medium fragility — a small number of HGV strikes can black out large areas).
• D (Data Resilience Index): 0 = all communications severed (EW + physical), 1 = satellite links and fibre alternatives fully operational. λ_D = 4.0 (high fragility — EW and cable strikes degrade rapidly).

R-layer effective contribution scales as √(E · D), not as their sum. If either component reaches zero, total R-contribution collapses to zero regardless of investment in the other. This multiplicative structure has a critical investment implication: a marginal euro in the weaker of E or D yields higher deterrence return than any increase in the stronger component.

Sensitivity analysis shows R-investment marginal benefit is 5–15× that of A-layer investment when R < 25% of budget, falling below 1× beyond R = 30–35%. The optimal R-layer threshold is therefore 25–30% — not arbitrary, but derived from the E×D multiplicative structure.

Critical operational threshold: Phase II C2 coherence (CI ≥ 0.6) requires both E ≥ 0.5 and D ≥ 0.5. Finland's estimated current state (E ≈ 0.3–0.4, D ≈ 0.4–0.5) places the system in Phase III under moderate operational stress.

Extension 2 — C2 Phase Transition Diagram

DRD-06 established the bifurcation condition AT_c = √(R/(1+α)). The phase transition diagram extends this to a two-axis representation:

• X-axis — Operational Stress (OS): composite of EW intensity, kinetic strike rate against A-layer nodes, sensor network degradation. Scale 0–1.
• Y-axis — C2 Cohesion Index (CI): 1.0 = fully coherent, 0.0 = collapsed.

Four operational phases:

• Phase I (CI 0.8–1.0, OS < 0.3): Coherent C2 — centralised common operating picture, linear decision chains.
• Phase II (CI 0.6–0.8, OS 0.3–0.6): Distributed but coherent — ACE fallback active, NATO ISR partially substituting national sensors. This is the target operational state for modern NATO C2.
• Phase III (CI 0.3–0.6, OS 0.6–0.8): Fragmented — common picture desynchronised, decisions devolve to local cells. A-layer loses network value non-linearly; R and G begin operating as independent systems.
• Phase IV (CI < 0.3, OS > 0.8): C2 collapse — no unified command, no shared situational awareness. F-35 operates as a local asset only; GBAD as point defence; R-layer determines survival, not outcome.

Hysteresis: The transition I→II→III→IV is rapid once OS crosses OS_c ≈ 0.6. Recovery from Phase IV to Phase II requires OS to fall to ≈ 0.4 — not 0.6 — because infrastructure, trust networks and dataflows do not restore automatically. Under balanced allocation (40A/35G/25R), recovery time from Phase IV is 5–7 days; under A-dominant allocation (60/20/10) it extends to 4+ weeks or becomes permanent.

NATO ISR contribution: alliance AWACS, AGS drones and F-35 datanet shift OS_c upward by approximately +0.10–0.15 under high US commitment. Under low US commitment (estimated p = 0.25 post-2025), this benefit disappears, restoring the case for maintaining national A-layer minimum at 30–35%.

Extension 3 — Minimax Equilibrium and Nash-Optimal Budget Allocation

Game-theoretic analysis of the attacker-defender interaction yields a stable result. Defining the adversary's strike vector α = (α_A, α_R, α_G) where α_i ∈ [0,1] and Σα = 1, the adversary's dominant strategy is A-layer priority (α_A ≈ 0.5–0.7) across all defender allocations tested. This is because A-layer fragility (λ_A = 5.0) ensures maximum expected damage per unit of strike capability regardless of defender posture.

Defender loss function under parallel strikes:

L = wA·(1 − exp(−λA·αA)) + wR·(1 − exp(−λR·αR)) + wG·(1 − exp(−λG·αG))

with weights w_A = 0.5, w_R = 0.3, w_G = 0.2.

Minimax analysis across allocation scenarios (S_A-column, adversary's dominant strategy):

• A-dominant (60/20/10): L = 0.82
• Balanced (40/35/25): L = 0.52
• DRD-dominant (20/40/40): L = 0.63

The balanced allocation (40A/35G/25R) is the Nash equilibrium: it minimises maximum adversary-achievable damage given the adversary's dominant strategy of A-layer strike priority. This confirms DRD-07's Scenario B result through an independent game-theoretic path — not as a heuristic but as a stable equilibrium.

Risk-adjusted optimum incorporating US commitment uncertainty: 35A/40G/25R, which maintains A-layer above the critical threshold for independent first-hour C2 coherence while increasing G-layer compensation for reduced NATO ISR availability.

Translating the preceding game-theoretic extensions to concrete adversary capabilities in 2026 produces a three-tier threat taxonomy with asymmetric implications for the A/G/R allocation framework.

The Avangard Discontinuity

Avangard is not a quantitative extension of the Kinzhal / Tsirkon threat — it represents a categorical discontinuity in the DAGRA framework. At Mach 20+ and 80–90 km altitude, no current or near-term GBAD system provides meaningful intercept probability. This has a direct structural implication: against Avangard, A-layer assets (F-35) and G-layer assets (Patriot, NASAMS, IRIS-T) are operationally irrelevant as defensive instruments.

The decision logic for Avangard employment also differs categorically: as a nuclear-armed strategic system, its use crosses a threshold governed by NATO's collective deterrence posture rather than conventional force exchange ratios. Its threat value therefore operates primarily through deterrence calculus, not through tactical engagement probability.

Against Avangard, two and only two responses are structurally coherent:

1. Deterrence: NATO nuclear umbrella and Article 5 — the alliance-level response that raises the cost of Avangard employment beyond the adversary's acceptable threshold.
2. R-layer survivability: If deterrence fails and a strike occurs, what critical C2, energy and data infrastructure survives? This is precisely the E×D decomposition from Extension 1 — the only investment that remains meaningful post-strike.

Implications for the 40A/35G/25R Allocation

The threat taxonomy reinforces the Nash-equilibrium allocation from Extension 3, but sharpens the rationale for each layer:

• A-layer (35–40%): Effective against the conventional threat spectrum — not against Avangard. F-35's primary value against hypersonic threats is as a NATO ISR node contributing to alliance-level deterrence signalling, not as an intercept platform.
• G-layer (35–40%): Kinzhal is the primary design case for GBAD investment. Patriot and NASAMS provide meaningful — if limited — intercept probability at Mach 10. Tsirkon is at the edge of G-layer effectiveness. Against Avangard, G-layer is irrelevant as an intercept mechanism but retains value as a conventional threat suppressor that preserves C2 coherence in Phase I–II.
• R-layer (25–30%): The only layer with structural relevance across the full threat spectrum including Avangard. Energy islanding, data redundancy (E×D), and distributed C2 are the sole meaningful investments against a nuclear HGV scenario. The marginal deterrence value of R-layer investment — through demonstrating second-strike survivability — is undervalued in conventional force planning frameworks.

Note on Avangard production: Russia has reported constraints on new system production, suggesting limited inventory depth. This does not reduce the strategic threat — a small number of Avangard strikes against Finnish C2 and energy infrastructure would be sufficient to achieve the operational objective of rapid systemic collapse. Limited inventory reinforces rather than diminishes the case for R-layer hardening.