Catalog
One page per mechanism, its defining formula, reference implementation, runnable demo, and the literature. Pick a mechanism:
A mechanism here pairs an aggregation
rule with a reward: it turns scattered private beliefs into a
price, probability, or decision and settles the payments that make
truthful participation worthwhile. The library also ships the pieces mechanisms
compose with, agent-side sizing (kelly), opinion pools and
calibration diagnostics (estimators with no reward), and margining (the
reward-enforcement leg, a partial mechanism with no aggregation of its own).
Scoring & elicitation
- Proper scoring rules, Log, Brier, spherical, pinball, CRPS, energy, truthfulness as a dominant strategy.
- Local (Hyvärinen) scoring rules, Score unnormalised densities with no partition function; the $m$-local rules and score matching.
- Scoring point-cloud submissions, Cotton's jittered-pin scoring of Monte-Carlo sample clouds: raw KDE settlement pays variance-shaving (the deconvolution incentive); jitter the outcome by the bandwidth and truth-telling is uniquely optimal.
- Peer prediction, Eliciting truth without ground truth (Bayesian Truth Serum).
- Forecast aggregation, Linear, logarithmic, and depth-trimmed opinion pools.
Markets & makers
- Parimutuel markets, Pool betting and Pennock's dynamic parimutuel market.
- Nearest-the-pin parimutuel, Cotton's continuous, density-pot-split pool over a continuum of outcomes; the reward engine behind monteprediction.com.
- Logarithmic Market Scoring Rule (LMSR), Hanson's logarithmic market scoring rule; bounded loss $b\log n$.
- Cost-function market makers, Any convex potential $C(q)$ is a no-arbitrage maker with prices $\nabla C$.
- Automated market makers (CFMMs), Constant-product / constant-mean CFMMs and impermanent loss.
- pm-AMM, parimutuel AMM for binary markets, Gaussian-score AMM for binary markets; price is a probability.
- Combinatorial & conditional markets, One LMSR over joint states; coherent marginals and "if B then A" conditionals.
- Decision markets, Conditional markets per action; ensemble the action-conditional forecasts and select (stochastic rules keep it truthful).
Auctions
- Continuous double auction, Price-time-priority limit order book.
- Frequent batch auction, Uniform-price batch clearing that neutralises the latency race.
- Hybrid CLOB + AMM, Complementary limit orders fill at zero slippage; an AMM backstops the remainder.
Derivatives
- Perpetual futures, No-expiry contract tethered to an index by a funding rate.
- Perpetual demand lending pools, Demand lending pools (GLP/JLP/HLP) with a target-weight mechanism.