Interactive demos
Each mechanism page carries its own Try it
widget, in context with the maths, running the JavaScript port in
docs/js/mechanisms.js, the same code checked for numerical parity
against the Python library in tests/test_js_parity.py, so the demos
never drift from the reference implementation.
Proper scoring rules
Score a two-outcome forecast (log / Brier / spherical) against the realised outcome.
Local (Hyvärinen) scoring
The score of a Gaussian quote, using only derivatives of log p, no normaliser.
Point-cloud scoring: jitter the pin
Raw KDE scoring pays you to shave h² off your variance; jitter the outcome and truthfulness wins.
LMSR
Buy shares; watch prices move, cost accrue, and the bounded maker loss.
Cost-function maker
A quadratic potential: prices are the gradient, LMSR's softmax is one choice among many.
Combinatorial market
An LMSR over two binary variables, keeping marginals and conditionals coherent.
Decision markets
Conditional values per action and a decision rule, argmax starves a market; softmax keeps all live.
Constant-product AMM
Sell into an x·y=k pool: output, new spot price, and impermanent loss.
pm-AMM
The prediction-market AMM price curve as a function of the reserve difference.
Parimutuel
Stakes set pool fractions (implied probabilities) and decimal odds, net of takeout.
Continuous double auction
A market buy sweeps the resting asks cheapest-first and walks up the book.
Frequent batch auction
One uniform clearing price per batch, maximising matched volume.
Hybrid CLOB + AMM
A YES buy fills complementary bids first, then spills into the LMSR backstop.
Perpetual futures
The funding rate that tethers a perp to its index, and who pays whom.
Demand lending pools
The linear funding rate that pushes long/short balance and price toward the index.
Peer prediction
Output agreement: reward matching reports, and its collusion failure mode.
Forecast aggregation
Linear vs logarithmic opinion pools of two categorical forecasts.