strataq · quantal response equilibria
Decide well when the other side is deciding too.
Prices, tenders, electricity offers, road tolls and budget splits are all the same shape of problem: your best move depends on theirs, and theirs on yours. Put in your costs, your grid and how demand behaves, and get the move to make, what it earns, and what would change it.
Your price, against a rival setting one too
liveThe profit at every price on this grid
| your price | expected profit |
|---|---|
| $1.19 | $50 |
| $1.29 | $66 |
| $1.39 | $75 |
| $1.49 | $77 |
| $1.59 | $73 |
| $1.69 | $66 |
| $1.79 | $57 |
| $1.89 | $47 |
Cheaper rival, softer price and a thinner margin; dearer rival, and the whole curve lifts. The recommendation never chases their price one-for-one, because they are choosing too. Open the studio to do this with your own numbers.
Four demos that do not exist anywhere else
Have your own rationality fitted by maximum likelihood while you play rock–paper–scissors; watch probability circulate on the nine joint states of a game and the entropy-production counter read exactly zero when it should; guess what real experimental subjects did; and put a game on the plane next to Sioux Falls, Dominick's and CAISO. Every one runs its mathematics live in the page.
Six problems, one solver
Each has its own page, its own inputs and a visual built for it. See them all
Pricing
What price do I set against a rival setting one too?
A price ladder with the profit curve over it.
/v1/solve/pricingAuction and tender
What do I bid in a sealed tender against one credible rival?
The distribution of bids, yours and theirs.
/v1/solve/auctionElectricity offers
What do I offer into a uniform-price market, and where does it clear?
The offer stack and the clearing cross.
/v1/solve/electricityTraffic assignment
Which link do I toll, and does the network get time back?
The Sioux Falls network with flow-weighted edges.
/v1/solve/routingBudget allocation
How do I split a fixed budget across contested accounts?
A Colonel Blotto grid, shaded by weight.
/v1/solve/allocationCoordination and standards
Three moves a side and a table of my own — which move?
The payoff matrix with its basins shaded.
/v1/solve/qreWho this is for
Pricing and revenue teams
You have a cost, a shelf and a competitor. You want the price, the margin it leaves, and the honest answer to what happens if their cost drops ten cents.
Bid and tender desks
You are one of a handful of credible bidders. You want the bid, the chance it wins, and what the surplus looks like a step either side of it.
Market and network operators
Generator offers into a uniform-price market, or traffic over a network with a toll on one link. You want the system total, not just your own line.
Analysts and researchers
Everything the app does is one HTTP call, and the same call from Python returns the same numbers. Fit the precision to your own observed choices first.
Start here
Solve
The studio: pick a problem type, put in your numbers, watch the answer move as you drag.
Open the studio →Bring your data
Upload or paste a CSV, map the columns, estimate what the data can pin down, then solve on it.
Load a file →API
Every endpoint, its schema, a live console and copyable curl and Python — read from the live service.
Open the console →Learn
What a precision is, why a distribution beats a point forecast, and where the method stops working.
Read the explainers →Test a rule over repeated rounds
A single solve answers one round. The backtest runs a hundred against a simulated rival and compares the solver's move with cost-plus, matching, best-reply-to-last and always-Nash on the same draws.
Open the backtest