Equilibrium Learning Mechanisms (EqLM)

When both players optimize, convergence matters.

Game-theoretic learning dynamics lie at the core of multi-agent systems: from mechanism design to neural network training. EqLM provides a research platform to study convergence via Magnetic Mirror Descent (MMD), Quantal Response Equilibria (QRE), mechanism truthfulness, and GPU-accelerated job orchestration — with full reproducibility tracking.

Core Games
4
Validated Findings
8
Reproducibility

The EqLM thesis

Convergence to Equilibrium

Beyond GDA's cycling behavior: Magnetic Mirror Descent with fixed or adaptive references reaches equilibrium on symmetric and asymmetric games. We trace the geometry of fixed points and validate log-linear convergence.

QRE Homotopy

Quantal response equilibria interpolate between randomness and perfect rationality. Warm-started homotopy paths accelerate solver convergence; adaptive damping handles high-rationality limits.

Mechanism Truthfulness

Token auctions studied via second-price vs. weighted aggregation. Empirical regret validates truthfulness: second-price is VCG-exact, weighted aggregation enables profitable manipulation.

Reproducible Science

Every result includes config hash, seed, git commit. Tarka verification gates findings; intermediate artifacts are stored and indexed. Full audit trail from hypothesis to sign-off.

GPU Acceleration

Training Studio orchestrates long-running jobs on CUDA. Experiments marshal PyTorch tensors, leverage implicit differentiation (DEQ), and track memory-efficient solver stacks.

Interactive Exploration

Tune hyperparameters in real time: method, learning rate, magnetic strength, rationality range. Animated convergence plots and strategy simplexes bring game dynamics to life.

Explore EqLM

Choose your path below to dive into equilibrium learning:

Equilibrium Lab

Run MMD, GDA, and QRE solvers on RPS, matching pennies, and biased games. Tune learning rate, magnetic strength, and step count; watch strategies converge.

QRE Explorer

Trace quantal response paths as rationality varies. See how agents shift from uniform randomness to best-response play; measure exploitability along the path.

Auction Playground

Design multi-agent token auctions. Compare second-price (truthful) vs. weighted aggregation; measure manipulation regret and output distributions.

Training Studio

Submit long-running jobs: solve-and-audit, ablations, hyperparameter sweeps. Monitor status, download results, and trace config hashes to reproducible runs.

Research Findings

Browse validated findings (F1–F8): convergence claims, mechanism properties, solver accelerations. All Tarka-reviewed with artifact paths and key numbers.

Technical Notes

  • Backend: FastAPI server (app/server.py) handles /api/solve, /api/qre_path, /api/auction, /api/jobs endpoints. Authentication via bearer token (GATEWAY_SECRET).
  • Frontend: Next.js 14 (app router) + React 18 + TailwindCSS. API proxy routes forward requests to gateway; replay mode serves canned demo data when offline.
  • Auth: Supabase SSR (optional). When NEXT_PUBLIC_SUPABASE_URL is set, sessions are maintained; otherwise auth softly disables and all pages are readable.
  • Reproducibility: Results stored in results/ directory; each experiment includes config hash, seed, and git commit. Tarka verification gates sign-off.
  • Deployment: Vercel (root dir apps/web). Environment variables: NEXT_PUBLIC_SUPABASE_URL, NEXT_PUBLIC_SUPABASE_ANON_KEY, GATEWAY_URL, GATEWAY_SECRET.