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strategies/s01_baseline_k8s_default.py)strategies/s02_resource_aware_heuristic.py)strategies/s03_stackelberg_equilibrium.py)strategies/s04_potential_game.py) ⭐ NOVELstrategies/s05_vcg_mechanism_design.py) ⭐ NOVEL| Property | S1 | S2 | S3 | S4 | S5 |
|---|---|---|---|---|---|
| Equilibrium existence | N/A | N/A | ✓ | ✓ | ✓ |
| Convergence guarantee | N/A | N/A | Conditional | ✓ Always | N/A |
| PoA bound | None | 2-approx | None | ≤ 5/3 | 1 (optimal) |
| Incentive compatible | ✗ | ✗ | ✗ | ✗ | ✓ |
| Decentralized | ✗ | ✗ | ✗ | ✓ | ✗ |
| Complexity | O(NM) | O(NM log N) | NP-hard | O(N²M·T) | NP-hard |
docs/mathematical_proofs.md — includes 15 theorems covering equilibrium existence, uniqueness, convergence rates, PoA bounds, and mechanism design properties.project/
├── core/
│ ├── system_model.py # Cluster, tenant, node, latency models
│ ├── payoff_engine.py # Cost functions, Nash verification
│ └── equilibrium_solver.py # CVXPY solver, best-response, PGD
├── strategies/
│ ├── s01_baseline_k8s_default.py
│ ├── s02_resource_aware_heuristic.py
│ ├── s03_stackelberg_equilibrium.py
│ ├── s04_potential_game.py # Novel
│ └── s05_vcg_mechanism_design.py # Novel
├── data/
│ └── synthetic_generator.py # Scenario generation (small/medium/large/xlarge)
├── evaluation/
│ ├── metrics.py # 30+ metrics (latency, fairness, SLA, isolation)
│ ├── visualizations.py # 8 plot types (CDF, radar, Pareto, heatmap, etc.)
│ └── statistical_tests.py # Wilcoxon, bootstrap CI, Friedman, Nemenyi
├── docs/
│ └── mathematical_proofs.md # 15 formal theorems with complete proofs
├── results/ # Generated plots and JSON results
├── run_all.py # Master evaluation runner
└── README.mdpython run_all.py --quickpython run_all.py --scenarios small medium large --seeds 30python run_all.py --scenarios medium --seeds 10 --output ./my_resultsnumpy scipy cvxpy matplotlib seaborn pandas networkxcong_j(x) = κ(ℓ_j/C_j)^p (polynomial, typically p=2)c_i = α·latency + β·contention + γ·isolationdocs/mathematical_proofs.md for complete formalization.