This repository explores the modeling of trust, coordination, and resilience in decentralized systems under adversarial conditions. It builds on research presented at the RSA Conference (RSAC) Security Scholar Program and serves as a foundation for ongoing work in simulation, formal methods, and distributed systems analysis.
Modern distributed systems operate in environments where participants are not uniformly rational or cooperative. This work studies systems composed of:
- Byzantine agents — arbitrary or adversarial behavior
- Altruistic agents — protocol-following, system-supporting behavior
- Rational agents — utility-maximizing behavior
Together, these form BAR (Byzantine–Altruistic–Rational) systems, which provide a more realistic model of decentralized coordination than classical assumptions of fully rational agents.
This repository investigates how trust, reputation, and coordination emerge in such systems using:
- Probabilistic modeling
- Markovian dynamics
- Game-theoretic frameworks
- Simulation-based analysis
A key clarification in this work:
The BAR framework is not a refinement of Nash Equilibrium in the traditional game-theoretic sense (i.e., it does not restrict the equilibrium set through stronger solution concepts such as subgame perfection or trembling-hand perfection).
Instead, it is better understood as an extension of equilibrium modeling:
- It expands the agent model beyond purely rational actors
- It incorporates heterogeneous behavioral types (Byzantine, altruistic, rational)
- It reflects real-world distributed systems where adversarial and cooperative behaviors coexist
In this sense, it can be viewed as a systems-level refinement—improving realism and robustness in equilibrium modeling—rather than a formal refinement within classical game theory.
Earlier versions of this work cited BAR-related results from a preprint (Reynouard et al., 2024). Those results have since appeared in a peer‑reviewed publication in Games and Economic Behavior (Gorelkina et al., 2025).
This repository now reflects the updated status of the research and situates BAR dynamics within the broader, evolving literature.
Published version:
Gorelkina, O., Laraki, R., & Reynouard, M. (2025). BAR Nash equilibrium and application to blockchain design. Games and Economic Behavior. https://doi.org/10.1016/j.geb.2025.09.008
Preprint version:
Reynouard, M., Laraki, R., & Gorelkina, O. (2024, January). BAR Nash equilibrium and application to blockchain design. HAL Open Science. https://doi.org/10.48550/arXiv.2401.16856
- docs/ Research artifacts (including RSAC poster)
- simulations/ Python-based models (planned)
- formal/ Lean4 and Haskell explorations (in progress)
- assets/ Diagrams and visual materials
This repository serves as a staging ground for:
- Simulation of trust and reputation dynamics in decentralized systems
- Exploration of equilibrium behavior under adversarial conditions
- Connections between game theory, distributed systems, and formal methods
- Early-stage work in formal verification and type-theoretic modeling
This is an active and evolving research repository.
Some components are exploratory and under development.
- Markov-based reputation system simulations (Python)
- Formal modeling of coordination dynamics (Lean4)
- Functional representations of system dynamics (Haskell)
- Integration of simulation results with theoretical frameworks
- Clustering Analysis -- Louvain clustering (modularity and compositionality) -- Leiden Clustering: Handles noisy or adversarial graph networks better (Byzantine resistant topology analysis) -- Spectral Clustering: Eigenvectors of Graph Laplacian (useful for consensconvergence
- Benford Law
- Centrality Analysis -- Degree Centrality (direct connections) -- Betweeness Centraligy (how often a node lies on shortest paths between other nodes) -- Closeness Centrality (How close a node is to other nodes in the network) -- Eigenvector (A node is important if it connects with other important nodes) -- Katz Centrality (Variant of Eigenvector) -- Harmonic (Improves cloness centrality for disconected nodes in the network) -- Load Centrality (Similar to betweeness, based on flow distribution across shortest path) -- Subgraph Centrality (Measures nodes involved in motifs/ cycles) -- Information Centrality (Impact of removing a node in the network)
- Extreme Value Analysis (Catastrophic Event on the left tail)
- Time series algorithms -- Stationary -- Cyclic, -- volatility, GARCH Volatility, & Variability -- Entropy (Hurst and Lyapanov) -- Autocorrelation and correlation -- Change Point: PELT, cummulative sum -- Spectral - FFT, Fourier Series -- Trend - Linear Trend, Polynomial Degree 2, Polynomial Degree 3, Detrend and apply Man Kendall and Theil Slope -- Seasonality
Ramamurthy Sundar