Distribution Markets for Trading Continuous Outcome Probabilities
Summary
The paper proposes distribution markets, prediction markets where traders express beliefs over a continuous range of possible outcomes rather than choosing among fixed options. Its example is a forecast of an event’s timing: participants can trade a full probability distribution over dates, allowing the market to convey uncertainty as well as a central estimate. The proposal aims to combine this richer expression with financial incentives for traders to improve a shared forecast.
The mechanism extends a constant function market maker from finite outcome tokens to function-valued positions. In the discrete illustration, the AMM’s reserves encode a distribution, and the paper uses an optimization argument to explain how trading can move them toward the market’s implied belief. For continuous outcomes, it adds solvency and collateral constraints, then discusses specializing distributions such as Gaussian forms to make computation practical. The paper provides mathematical constructions and numerical collateralization methods, but no empirical market results. Practical viability depends on distribution restrictions, accurate collateral checks, and efficient on-chain implementation.
Key ideas
- Traders can express beliefs across a continuous outcome range instead of selecting preset bins.
- The proposed AMM represents positions as functions that pay according to the realized outcome.
- In the discrete construction, market reserves can be interpreted as an implied probability distribution.
- Continuous markets require solvency and collateral constraints beyond a simple norm invariant.
- Restricting trades to standard distribution families can make implementation more computationally practical.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.