What is an AMM (LMSR)?

Explained, with an example

In LMSR the market maker's cost function depends on the number of shares sold for each outcome, prices always sum to 1, and the sponsor's maximum loss is bounded by the liquidity parameter b times ln(number of outcomes) ^[1]. A larger b means deeper liquidity but a bigger possible subsidy. Play-money site Manifold describes combining limit orders with an AMM ^[2].

Formula

cost C(q) = b · ln( Σᵢ e^(qᵢ / b) )
price pᵢ = e^(qᵢ / b) / Σⱼ e^(qⱼ / b)
max market-maker loss = b · ln(n)

Related terms

• Order book (CLOB) — An order book is the list of open buy (bid) and sell (ask) orders for a contract, matched by price and time; a central limit order book (CLOB) is the electronic version most exchanges use.
• Liquidity — Liquidity is how easily you can buy or sell without moving the price; the CFTC describes a liquid market as one where trades happen with minimal effect on price.
• Market maker — A market maker continuously quotes both a buy and a sell price, earning the spread in return for providing liquidity and absorbing temporary order imbalances.
• Prediction market — A prediction market is an exchange where people trade contracts whose payout depends on whether a future event happens, so the trading price can be read as the crowd's probability estimate.

Frequently asked questions