Agents play quantum games
on classical compute.

No qubits needed.

A walkthrough of multi-agent LLMs operating as mathematical-physics operators — the agent proposes, the eigenvalue disposes. Agents compose Baba is Quantum rules — the [SUBJECT][VERB][PROPERTY] compositional grammar — that route to quantum-mechanical operations on the unified Hamiltonian. Cooperation is the ground state. The Care operator scores cooperative equilibria; the scale coupling tensor carries discoveries across scales.

Stag Hunt — Quantum Game Theory in One Picture

How “pick one” becomes “pick both”

CLASSICAL (Nash Equilibrium)

Hunter A
├── 🦌 Stag (needs both)
└── 🐰 Hare (safe) ✓
Hunter B
├── 🦌 Stag (risky)
└── 🐰 Hare (safe) ✓
🐰🐰 Both pick Hare — stable but suboptimal

QUANTUM (Cooperative Equilibrium)

HUNTER A 🦌 🐰 interference 🦌🦌 cooperate 🦌 🐰 HUNTER B
🦌🦌 Both hunt Stag — cooperation is ground state
Superposition
Explore all strategies simultaneously
Entanglement
Agents’ choices become correlated
Interference
Amplify synergy, suppress trade-offs

The games agents play

Each game is a mechanism from the published quantum game theory literature, deployed on classical compute via Baba is Quantum.

Foundation — running now

EWL Entangled Games (Eisert, Wilkens, Lewenstein, 1999). Agents share an entangled initial state and apply unitary strategies. At maximal entanglement, mutual cooperation is the Nash equilibrium — a strategic regime classical games cannot reach.

Parrondo's Compositional Pipelines (Kadiri, 2024). Two individually losing strategies, composed, produce a winning outcome. Baba is Quantum's multi-stage pipelines instantiate the paradox: grammar composition creates winning strategies that no individual operation contains.

GHZ Coordination Games. Three players sharing a GHZ state always satisfy joint constraints that classical independent players satisfy 75% of the time. The trapped ion proof of concept instantiates this cooperation structure at N = 3.

Stag Hunt. The choice between safe individual optimization (the hare) and risky collective coordination (the stag). The demo shows the stag pays off.

Generalization demo

Bayesian Games (Brunner & Linden, 2013). Agent blindness is Bayesian incomplete information: agents see formulas plus mathematical-state feedback, never raw properties. The Hamiltonian evaluates the experiments — agents cannot game what they do not compute.

Price of Anarchy (Scarpa, 2010). Optimal welfare divided by worst-case independent welfare. As the shared grammar expands, PoA falls — intelligence compounds, and the proof is a mathematical inequality.

Shapley Value (Burge, Barbeau & Garcia-Alfaro, 2023). Each agent's marginal contribution to the grand coalition. Superadditivity of the multi-agent game — and the per-layer contribution when Layer 1 and Layer 2 are evaluated together.

Bell / CHSH Synergy Detection. Bell-state purity on agent pairs. CHSH S > 2 violates the classical bound (quantum reaches up to 2√2 ≈ 2.83). Synergy is measurable, not asserted.

Mechanism Design (Revelation Principle). The Hamiltonian is the mechanism designer. Agents report; the eigenvalue authenticates. Truth-telling is the dominant strategy — because eigenvalues do not respond to strategy.

Layer 1 → Layer 2 — the generalization demo

Proof-of-concept: the 7-layer trapped ion quantum computing stack — host materials · crystal prototyping · optical interfaces · Rydberg gates · error correction · quantum memory · modular networking.

Validation engine — math transfers by isomorphism to the $1.5T+ enterprise verticals.

The demo runs the same games at Layer 1 and Layer 2 — same engine, different layers, different properties, different data. Only the per-layer scoring curves change. The engine doesn't know which layer it's evaluating.

Layer 1 · Host Materials

Agents play EWL, GHZ, Parrondo, and Stag Hunt over candidate host materials. Cooperative equilibria emerge across competing materials properties — the foundation grammar is built.

Layer 2 · Crystal Prototyping

No retraining. No weight changes. No new agents. Patterns Layer 1 authenticated propagate forward through the scale coupling tensor and the conceptual layer of the three-layer quantum interference memory. The same games run again over crystal-prototyping properties — and Bayesian Games, Price of Anarchy, and Shapley Value quantify whether the grammar genuinely transferred. Parrondo, Shapley, GHZ, and Mechanism Design at the cross-layer level reveal compounds neither layer alone can find.

Same engine. New adapter. No retrained model.

Patent Pending

Data provenance. Layer 1 candidates read from Materials Project (CC BY 4.0) — the canonical open DFT-computed inorganic-compound database. Layer 2 candidates read from AFLOW with the ICSD experimental-synthesis filter. Htotal computes on real crystallographic data — agents never see the underlying property values, only chemical formulas and mathematical-state feedback.

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