Automated Market Makers
Definition
An automated market maker (AMM) is a pricing formula that always stands ready to trade, setting a price from the quantities already sold. In prediction markets the best-known design is Robin Hanson's logarithmic market scoring rule (LMSR), which prices each outcome so that prices sum to $1 and move with every purchase. Hanson describes AMMs as playing the market maker's role 'for the price of a modest subsidy.'
Why it matters
AMMs guarantee a price for any trade, which helps thin markets, but the price moves with size by formula and the sponsor subsidizes the information. Investors trading against an AMM should calculate their price impact before trading and know who funds the liquidity and on what terms.
Common misconceptions
- •An AMM price is not a consensus of resting orders; it reflects cumulative net purchases.
- •Always-available liquidity is not free; price impact grows with size.
- •Kalshi and Polymarket's main markets use order books, not AMMs.
- •The label is only a starting point. Investor outcomes usually depend on the governing documents, cash-flow priority, valuation policy, disclosure quality, and manager discretion surrounding the term, not just the shorthand definition used in marketing materials.
Technical details
Worked example: LMSR, two outcomes, b = 100
Start at 50/50: no shares sold.
Buy 50 yes: cost = 100 ln(e^0.5 + 1) - 100 ln 2 = $28.09, an average of 56.2 cents; the yes price moves to 62.2 cents.
Buy 200 yes from the start instead: cost $143.38, average 71.7 cents; the price moves to 88.1 cents.
Maximum sponsor loss: 100 ln 2 = $69.31.
How investors apply the term
Investors usually apply this term by tying the definition back to the controlling documents and then asking which cash flows, rights, restrictions, or valuation assumptions it changes. A useful review looks at the term alongside fees, leverage, liquidity, reporting frequency, and manager discretion rather than treating it as a standalone concept.
The practical diligence test is simple: identify who benefits if the assumption is wrong, who has control when conditions change, and what evidence the investor receives after closing. Terms that cannot be reconciled to documents, cash movements, and monitoring data should be treated as marketing shorthand until proven otherwise.
Frequently asked questions
- How does an automated prediction market differ from an order book?
- An order book matches traders with each other; an AMM is always the counterparty. Polymarket uses 'a Central Limit Order Book' in which 'prices aren't set by Polymarket - they emerge from supply and demand as users trade with each other.' An AMM quotes a price for any size at any time, with price impact set by the formula rather than by resting orders.
- How does LMSR set prices?
- From a cost function. With quantities q sold for each outcome and a liquidity parameter b, the cost is C(q) = b x ln(sum of e^(q_i/b)), a trade costs the change in C, and each outcome's price is e^(q_i/b) divided by the sum. Larger b means deeper liquidity and smaller price moves.
- Who pays for the liquidity?
- The sponsor. Because the AMM always trades, it can lose to informed traders. For LMSR the worst case is bounded: with n outcomes it is b x ln(n), which follows from the cost function. A two-outcome market with b = 100 can lose at most about $69.31.