Sovereignty as Strategic Games: A Distributionally Robust Approach

Overview

This repository implements a game-theoretic framework for supplier dependency and sovereignty decisions under political risk. The core thesis: sovereignty is not a static cost-benefit problem but a dynamic sequential game between the firm and Nature, where Nature represents adversarial political/regulatory dynamics.

Documentation

Core Materials

• Main Notebook: sovereignty_dp_cvar_wasserstein_ultraCFO.ipynb - CFO-friendly walkthrough with executive summary
• Game Theory Tutorial (EN): docs/game_theory_tutorial.md - Comprehensive guide on game theory, minimax, Bellman equations, and n-player extensions
• Tutoriel Theorie des Jeux (FR): docs/game_theory_tutorial_fr.md - Version francaise complete

Strategic Framework (v2.0)

• Unified Framework: docs/bellman_wasserstein_mean_field_framework.md - Comprehensive presentation of the Bellman-Wasserstein Mean-Field framework for strategic autonomy, including multi-criterion analysis, hierarchical game structure, and governance integration
• Implementation Roadmap: docs/implementation_roadmap.md - Phased roadmap (18-24 months) to transform the toy model into a production-grade Strategic Autonomy Operating System

Why Games?

Traditional real options frameworks (Dixit & Pindyck, 1994) treat uncertainty as exogenous random shocks. This misses the strategic dimension: political actors respond to firm actions, regulatory regimes exhibit persistence and switching dynamics, and forecast errors are not random but potentially adversarial.

We model sovereignty as a finite-horizon Markov game:

• Player 1 (Firm): Chooses actions {wait, invest, hedge, accelerate, exit} to minimize cost
• Player 2 (Nature): Controls tariff regime transitions and, under ambiguity, selects adversarial next-state distributions within a Wasserstein ball

This framing captures:

1. Strategic optionality: The firm's decision is a policy (state-contingent action rule), not a one-time choice
2. Ambiguity aversion: Nature can shift transition probabilities within an uncertainty set, forcing robust policies
3. Path dependence: Migration progress, investment sunk costs, and hedge effectiveness evolve endogenously

Mathematical Formulation

State Space

State $s = (\tau, m, \mathbf{f})$ where:

• $\tau \in {0,1}$: tariff regime (off/on)
• $m \in {0, \ldots, M}$: migration progress (years to exit)
• $\mathbf{f} = (i, h, e)$: binary flags for investment started, hedge active, exit exercised

Action Space

Firm chooses $a_t \in \mathcal{A} = {\text{wait}, \text{invest}, \text{hedge}, \text{accelerate}, \text{exit}}$

Nominal Dynamics

Tariff transitions follow a parameterized Markov chain: $$P(\tau_{t+1} = 1 | \tau_t = 0) = p_{01}, \quad P(\tau_{t+1} = 0 | \tau_t = 1) = p_{10}$$

Migration progress evolves deterministically: $m_{t+1} = \min(M, m_t + \Delta_m(a_t))$

Flags update based on actions and progress (see notebook for full transition kernel).

Objective: Robust CVaR

We solve for the policy $\pi^*$ that minimizes worst-case tail risk: $$V_t(s) = \min_{a \in \mathcal{A}} \sup_{p \in \mathcal{P}{\varepsilon(t)}(p_0)} \text{CVaR}\alpha^p \left[ \gamma_t \ell(t, s, a) + V_{t+1}(S') \right]$$

where:

• $\text{CVaR}_\alpha$: Conditional Value-at-Risk at level $\alpha$ (tail-risk measure)
• $\mathcal{P}_{\varepsilon}(p_0)$: Wasserstein ball of radius $\varepsilon$ around nominal distribution $p_0$
• $\ell(t,s,a)$: stage cost (CAPEX + OPEX + tariff exposure + exit costs)
• $\gamma_t = (1+r)^{-t}$: discount factor (WACC-based)

The Wasserstein distance constraint ensures robustness to forecast errors while avoiding worst-case conservatism of full minimax approaches.

Key Innovations

1. Progressive Hedge Effectiveness

Unlike binary hedge models, we implement $\eta(m) = m/M$ effectiveness scaling: hedge value increases with migration progress, capturing the business reality that alternative suppliers become more viable as you build relationships and dual-source.

2. Time-Varying Ambiguity

The ambiguity radius $\varepsilon(t)$ is linked to observable political risk indicators: $$\varepsilon(t) = \varepsilon_{\min} + (\varepsilon_{\max} - \varepsilon_{\min}) \cdot R(t)$$ where $R(t) \in [0,1]$ could be calibrated to policy uncertainty indices (Baker et al., 2016), election cycles, or trade negotiation windows.

3. Separation of Risk and Ambiguity

The model distinguishes:

• Risk (Level 1): Tail events under known distribution → CVaR optimization
• Ambiguity (Level 2): Unknown distribution within Wasserstein set → DRO

This separation is critical for correct pricing of uncertainty (Gilboa & Schmeidler, 1989; Hansen & Sargent, 2008).

Extensions Beyond Toy Model

The current implementation simplifies:

1. Binary tariff regime: Real tariffs have magnitude, gradual phase-in, and sectoral heterogeneity
2. Single supplier: Multi-supplier portfolios require network flow formulation
3. Deterministic migration: Add learning-by-doing (Arrow, 1962) and implementation risk
4. Exogenous transitions: Endogenize political response to firm actions (leader-follower structure)
5. Perfect state observability: Add partial observability (POMDP formulation)

Production extensions should:

• Calibrate transition probabilities to historical trade policy data
• Link $\varepsilon(t)$ to market-implied ambiguity (option skew, credit spreads)
• Add capacity constraints and organizational friction
• Model competitive dynamics (oligopoly migration game)
• Incorporate learning: Bayesian update of $p_{01}, p_{10}$ as tariff regime unfolds

Related Literature

Game Theory Foundations

• von Neumann, J., & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
• Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1), 48-49. DOI: 10.1073/pnas.36.1.48
• Fudenberg, D., & Tirole, J. (1991). Game Theory. MIT Press.

Dynamic Programming and Bellman Equations

• Bellman, R. (1957). Dynamic Programming. Princeton University Press.
• Puterman, M. L. (2014). Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons.
• Shapley, L. S. (1953). Stochastic games. Proceedings of the National Academy of Sciences, 39(10), 1095-1100. DOI: 10.1073/pnas.39.10.1095

Real Options and Investment Under Uncertainty

• Dixit, A. K., & Pindyck, R. S. (1994). Investment under Uncertainty. Princeton University Press.
• Trigeorgis, L. (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. MIT Press.

Robust Optimization and Distributional Robustness

• Ben-Tal, A., El Ghaoui, L., & Nemirovski, A. (2009). Robust Optimization. Princeton University Press.
• Kuhn, D., Mohajerin Esfahani, P., Nguyen, V. A., & Shafieezadeh-Abadeh, S. (2019). Wasserstein distributionally robust optimization: Theory and applications in machine learning. Operations Research, 67(6), 1373-1416. DOI: 10.1287/opre.2019.1902
• Blanchet, J., & Murthy, K. (2019). Quantifying distributional model risk via optimal transport. Mathematics of Operations Research, 44(2), 565-600. DOI: 10.1287/moor.2018.0936

Risk Measures and CVaR

• Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. DOI: 10.1016/S0378-4266(02)00271-6
• Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. DOI: 10.1016/S0378-4266(02)00269-8

Decision Theory Under Ambiguity

• Gilboa, I., & Schmeidler, D. (1989). Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18(2), 141-153. DOI: 10.1016/0304-4068(89)90018-9
• Hansen, L. P., & Sargent, T. J. (2008). Robustness. Princeton University Press.
• Maccheroni, F., Marinacci, M., & Rustichini, A. (2006). Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica, 74(6), 1447-1498. DOI: 10.1111/j.1468-0262.2006.00716.x

Policy Uncertainty and Economic Impact

• Baker, S. R., Bloom, N., & Davis, S. J. (2016). Measuring economic policy uncertainty. Quarterly Journal of Economics, 131(4), 1593-1636. DOI: 10.1093/qje/qjw024
• Handley, K., & Limão, N. (2015). Trade and investment under policy uncertainty: Theory and firm evidence. American Economic Journal: Economic Policy, 7(4), 189-222. DOI: 10.1257/pol.20140068

Learning in Dynamic Environments

• Arrow, K. J. (1962). The economic implications of learning by doing. Review of Economic Studies, 29(3), 155-173. DOI: 10.2307/2295952

Implementation Details

Language: Python 3.11+
Key Dependencies:

• cvxpy: Convex optimization for Wasserstein DRO inner problem
• numpy: Numerical linear algebra
• pydantic: Type-safe parameter specification

Solver: CLARABEL (primary) with SCS fallback for conic programs (Wasserstein optimal transport)

• CLARABEL: Modern Rust-based conic solver with excellent numerical stability
• SCS: Splitting Conic Solver as fallback for robustness

Computational Complexity: $O(T \cdot |S| \cdot |A| \cdot n_{\text{LP}})$ where:

• $T$: horizon length (10 years)
• $|S|$: state space size (64 states)
• $|A|$: action space size (5 actions)
• $n_{\text{LP}}$: LP solve time for Wasserstein ball projection (~10-50ms)

For horizons $T > 20$ or state spaces $|S| > 1000$, consider approximate DP methods (fitted value iteration, deep RL).

Usage

For CFOs and Business Leaders:

• Start with the main notebook sovereignty_dp_cvar_wasserstein_ultraCFO.ipynb
• Jump to Section 9 for results and Section 11 for interpretation
• Review Executive Summary at the end for AI-generated synthesis

For Quant Teams:

• Read docs/game_theory_tutorial.md for theoretical foundations
• Focus on notebook Sections 2-8 for methodology
• Review Section 10 for sensitivity analysis

For French Speakers:

• Voir docs/game_theory_tutorial_fr.md pour guide complet 🇫🇷

Parameter Calibration:

1. Estimate $(p_{01}, p_{10})$ from historical tariff transition data or political risk scores
2. Set $\varepsilon(t)$ based on option-implied volatility skew or analyst forecast dispersion
3. Calibrate costs to actual supplier contracts and migration cost estimates
4. Validate CVaR level $\alpha$ against firm's risk appetite (typically 0.90-0.95)

Citation

If you use this framework in research or production models, please cite:

@misc{sovereignty-games-2026,
  title={Sovereignty as Strategic Games: A Distributionally Robust Approach to Supplier Dependency},
  author={Jean-Baptiste Dézard},
  organization={Deal ex Machina SAS},
  year={2026},
  howpublished={\url{https://github.com/jeanbaptdzd/DP-CVaR-Wasserstein}},
  note={First draft toy model for strategic decision analysis under political risk}
}

Author

Jean-Baptiste Dézard
Deal ex Machina SAS

License

This work is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

You are free to:

• Share: copy and redistribute the material in any medium or format
• Adapt: remix, transform, and build upon the material for any purpose, even commercially

Under the following terms:

• Attribution: You must give appropriate credit, provide a link to the license, and indicate if changes were made

Contact

For technical questions regarding this framework, please open an issue on the GitHub repository.

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Disclaimer: This is a first-draft toy model for research and education purposes. Not intended for direct production use without extensive validation, calibration, and risk management review.

Important: This is vibe research - it may contain slop. Use at your own risk :)