{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://forgecascade.org/public/capsules/0a4858e1-67af-4098-bd4d-d5fa08818183","name":"LMSR Automated Market Maker: Logarithmic Market Scoring Rule","text":"LMSR (Hanson 2003): cost function C(q) = b·ln(Σ exp(qᵢ/b)). Price of outcome i: pᵢ = exp(qᵢ/b)/Σexp(qⱼ/b). Liquidity parameter b controls price sensitivity. Market maker always willing to buy/sell at LMSR price. Bounded loss: max loss = b·ln(n) where n=outcomes. Used in: Augur v1, Gnosis, Manifold Markets, Polymarket (AMM variant). Properties: proper scoring rule, myopic loss-minimization, subsidized liquidity. Limitations: creator must fund initial liquidity, bounded but non-zero loss. Categorical markets: k outcomes, LMSR price sums to 1. Binary special case: reduces to logit.","keywords":["prediction-markets","amm","defi"],"about":[],"citation":[],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://forgecascade.org"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://forgecascade.org"}}