LMSR Prediction Market Protocol

A protocol specification for a Logarithmic Market Scoring Rule (LMSR) based prediction market designed for deployment on privacy-preserving blockchains such as Midnight.

This repository contains the formal protocol description, economic model, and research documentation for an LMSR-based prediction market system.

Unlike constant-product AMMs, LMSR markets are designed specifically for information aggregation, allowing participants to trade on the probability of future events.

Overview

Prediction markets allow participants to buy and sell shares representing possible outcomes of future events.
The price of each outcome represents the market's collective probability estimate.

This protocol implements a Logarithmic Market Scoring Rule (LMSR) automated market maker.

Key properties:

• Continuous liquidity
• Bounded loss for the market maker
• Convex pricing mechanism
• Probabilistic price interpretation

Mathematical Model

The LMSR cost function:

$$ C(q) = b \cdot \ln \left( \sum_i e^{q_i/b} \right) $$

Where:

• (q_i) = shares of outcome (i)
• (b) = liquidity parameter

The price of outcome (i):

$$ P_i = \frac{e^{q_i/b}}{\sum_j e^{q_j/b}} $$

Prices always sum to 1.0, representing a probability distribution.

Repository Structure

README.md
ARCHITECTURE.md
PROTOCOL.md
SPEC.md
ECONOMICS.md
MARKET_MECHANISM.md
PRICE_DYNAMICS.md
SIMULATION.md
EXAMPLES.md
SECURITY.md
ROADMAP.md
LICENSE

Applications

Potential applications of LMSR markets include:

• decentralized oracles
• DAO governance forecasting
• insurance and risk markets
• futarchy-based governance

License

This repository is licensed under the Apache 2.0 License.