SAGE¶
A computational framework for stochastic strategic interaction: Nash and quantal-response equilibria, potential and non-potential games, entropy-regularised response, and non-equilibrium strategic dynamics, with empirical estimation across pricing, energy, congestion and allocation domains.
The library is strataq (import strataq, never import sage — SageMath owns that name).
SAGE builds measuring instruments for strategic systems and points them at things:
| Instrument | Reads | Status |
|---|---|---|
chi_equilibrium |
how equilibrium play responds to a payoff perturbation — the strategic resolvent (I − SB)⁻¹S | Stage 1 |
reciprocity_defect (ℛ) |
asymmetry of that response: exactly 0 on potential games, rising with harmonic content; λ-free | Stage 1 |
strategic_spectrum |
eigenvalues of SB: distance to criticality, bifurcation type | Stage 1 |
entropy_production_rate |
dissipation of the strategic dynamics: 0 iff detailed balance | Stage 1 |
alpha |
harmonic fraction of the (normalised) game via the separable Hodge transform | Stage 1 |
Where they get pointed: systems where the answer is known (congestion networks — exact potential, α = 0; Colonel Blotto — strongly non-potential), where it matters commercially (retail pricing, electricity bidding), and where nobody has looked.
- Progress dashboard — what works now, gate states, claim ledger.
- Concepts — the confidence tiers every claim carries.
- Architecture patterns — how the code is built.
Pre-alpha; the library reaches PyPI when Stage 1 gates are green.