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The landscape

Deployed contest platforms, prediction markets, and the mechanisms they run, classified by what participants submit, how it settles, whether an aggregation stage exists, and what state threads between rounds. Surveyed July 2026; corrections and additions welcome by PR.

The classification follows the algebra paper: a stage consumes reports, threads a state (wealth, reputation, stake), and emits an aggregate plus transfers. Multi-stage below means one mechanism's output is the priced or scored object of another, not merely a repeated game. The Chaining column marks entries with that structure, and any column header can be clicked to sort. One further axis matters: whether the reused output is a point (a price, a projected winner), which is ordinary derivative structure, or probabilistic (a distribution, percentile, rank), which is rare; the closing section keeps the two apart. Statuses with (?) could not be fully verified.

Probability markets

Polymarket also lists markets whose subject is a named forecaster's output (the Nate Silver markets of 2024 onward): a real-money market on a forecast, which is a genuine two-stage structure. Dispute layers (UMA's optimistic oracle resolving Polymarket, Kleros appeals, Reality.eth bond escalation) are staged bonded games on a first-stage answer rather than second-stage markets.

Forecasting tournaments and polls

Quant and staked tournaments

Crypto forecasting networks

Totes

The tote is the oldest margins-and-dependence market structure we know of, and it is parallel, not chained: marginal and joint pools run simultaneously on the same races, neither settling on the other's output, with consistency between them left to arbitrage. The documented win-versus-exotic strategies (Hausch–Ziemba–Rubinstein and successors) are that consistency trade.

Financial-market analogues

The structures, kept distinct

Chained on point outputs (one market's price is the settled object of another): every derivative, and in electricity the virtual bids and FTRs written on day-ahead prices; Polymarket's markets on Nate Silver's projected winner; Numinous scoring against Polymarket resolutions; Allora's second tier predicting the first tier's losses; Numerai paying marginal contribution to its meta-model. These are translations of a point output, ordinary derivative structure, ubiquitous and old.

Chained on probabilistic outputs (one mechanism's distribution, percentile, or rank becomes the message or settlement transform of another): the retired microprediction platform's z-streams and dependence streams. Manifold's resolves-to-market markets settle one market at another's displayed probability, which for a binary event is its whole distribution, but with no exogenous outcome anywhere in the chain there is no proper scoring anchor: the equilibrium is indeterminate, and these run as play-money beauty contests. We know of nothing else.

Parallel factored (margins and dependence in separate simultaneous books, neither settling on the other, consistency left to arbitrage): the racetrack tote's win versus exotic pools; index versus single-name option books (dispersion); tranches versus single-name CDS (base correlation). Separate pools are not chaining; the books can disagree, and the documented strategies trade the disagreement.

Repeated with threaded wealth (one game, state carried across rounds): monteprediction, and the totes and exchanges round by round.

Nothing live chains probabilistic output, distributional elicitation into residual or dependence markets with wealth as the routed state. That gap is the subject of the algebra paper's open problems.