Is this market a landscape — or a whirlpool?
Some strategic systems are like water finding its level: everyone adjusts, things settle, and the settling point is a genuine equilibrium. Others never settle — strategy chases strategy in circles forever, like rock beats scissors beats paper beats rock. From the outside the two can look identical. This project builds meters that tell them apart. Five minutes, four instruments, real data at the end.
First: nobody plays perfectly
Classical game theory says: pick the best action, with probability one. Real decision makers are payoff-sensitive, not payoff-perfect — better options get chosen more often, by an amount set by one dial, λ. Slide it: at the left everything is noise, at the far right you recover the classical answer. Everything else in this tour lives between those extremes.
At λ ≈ 0 every price is equally likely; slide right and probability piles onto the argmax. Notice the 2-points-behind price keeps real probability long after the 13-points-behind one is gone — magnitude matters, which is exactly what Nash throws away.
Everyone's noise responds to everyone's noise
Your mix of choices shapes their payoffs; their mix shapes yours. Click inside the triangle to drop a population anywhere and watch the loop run. On the coordination game it rolls downhill and stops — a landscape. On rock–paper–scissors it circulates — a whirlpool. Same math, opposite fates.
harmonic: trajectories spiral around the centre — the circulation the dissipation meter measures. The quantal response equilibrium is where the flow stops moving — watch it drift from the uniform centre (λ small) toward a Nash equilibrium (λ large).
Still water or turning water — measured, not assumed
Here is the whole joint system as a lattice: every combination of choices, with probability as node size. In a landscape game the probability flow is still — every edge carries equal traffic both ways. In a whirlpool game the amber current runs one way around, forever, and the entropy-production meter reads it in nats. This is the live solver computing the exact stationary state — and the button estimates the same number from sampled trajectories alone, which is what makes real data reachable.
You can measure this without knowing anyone's payoffs
The payoffs are hidden in real systems. The meter that survives that: poke one player's incentives, read how the other moves; then poke the other, read the first. On a landscape the two cross-readings agree exactly — a deep symmetry from physics (Onsager reciprocity). On a whirlpool they disagree, and the disagreement is the measurement. Switch the game and watch the badge flip.
potential game — the two cross-readings must AGREE (Onsager reciprocity). This works without knowing the payoffs: only pokes and observed shifts — that is why ℛ is estimable from real pass-through data. Slide λ: the asymmetry's MAGNITUDE changes, but zero stays zero and nonzero stays nonzero at every λ — the symmetry verdict is λ-free.
So — what do real systems read?
A real road network (Sioux Falls, with its actual demand table) reads exactly zero — traffic is a landscape, to machine precision, and you can toll any link to feel the symmetry: the routing scenario. A real power market (CAISO, July 2026) reads as a measurably driven cycle — the day-ahead price loop dissipates about 1.1 nats per day, concentrated exactly in the scarcity weeks, a finding that survived four null models and one retraction: the market reading.
Landscape or whirlpool is not a modelling assumption. It is a quantity you measure — and everything above regenerates from fixed seeds in the open repository, wins and retractions alike: the anomaly log.