How Automated Market Makers Price Prediction Market Outcomes

A concrete scenario: buy one Yes at $0.62 and the AMM moves the price to $0.65

Imagine a simple Yes/No prediction market for Event E. The AMM currently quotes the Yes contract at $0.62. You decide to buy one Yes contract. After your trade the AMM’s marginal price for Yes rises to $0.65.

Keep these numbers in mind and return to them through the rest of the explanation.

Outcome	What you paid	Settlement if Event E happens	Net before fees
You buy 1 Yes at $0.62	$0.62	$1.00	+$0.38
You buy 1 Yes at $0.62	$0.62	$0.00	−$0.62
Next buyer’s marginal price	—	—	$0.65 quoted after your purchase

This tiny table is the worked example we carry through: entry price $0.62, one contract purchased, new quoted price $0.65, payoff $1 if the event happens.

Running the numbers: cost, payoff and price impact

Start with the immediate cash flows. You pay $0.62 to the AMM for one Yes contract. If Event E occurs, that contract settles at $1 and you receive $1, so your gross gain is $0.38. If Event E does not occur, the contract expires worthless and your loss is $0.62.

The AMM’s quoted price is the marginal price: the cost for the next infinitesimal unit. Your single-contract purchase changed the AMM’s internal state and therefore the marginal price. In this scenario the quoted Yes price rose from $0.62 to $0.65. That 3¢ difference is the observable price impact (slippage) from your trade.

Price impact scales with trade size and liquidity settings. For the same market and rule, a higher-liquidity parameter can make the same one-contract buy move the price only 0.5¢ instead of 3¢. Conversely, a low-liquidity setting could make that buy move the price 10¢. The movement amount depends wholly on the AMM’s pricing rule and its liquidity parameter.

How an AMM always has a price (and how that differs from an order book)

An automated market maker (AMM) is a fixed formula that converts the market’s stored quantities into a marginal price. The AMM keeps a notion of outstanding Yes and No shares (or, in some designs, a single quantity per outcome). A cost function or scoring rule maps those quantities to a cost; its derivative gives the marginal price.

Because the rule is fixed and public, the AMM can quote a price at any time without waiting for a counterparty to post an order. Buying from the AMM changes the stored quantities and therefore the marginal price for future trades; that built-in feedback is why AMMs provide continuous prices and why larger trades move prices more.

Compare that with a traditional order book, where prices exist only when counterparties post matching orders. The practical differences are summarized below.

Feature	AMM (bonding curve / market-scoring rule)	Traditional order book
How a price appears	From a fixed mathematical function (cost or scoring rule)	From matching explicit buy/sell orders from users
Liquidity guarantee	Always available; the AMM will trade against you	Depends on displayed orders and other traders
Price predictability	Deterministic given curve and parameters	Unpredictable; depends on other traders' willingness to fill orders
Price impact (slippage)	Explicit and smooth: larger trades move price by design	Variable: large market orders can clear many price levels
Who sets the spread	Implicit in the curve and its liquidity parameter	Traders set bid/ask; market makers can change spread dynamically
Typical cost to platform	Protocol funds or liquidity providers subsidize depth	Less predictable funding needs; fees incentivize makers/takers

Keep the $0.62→$0.65 example in mind: the AMM quoted $0.62 because its cost function implied that marginal price given current outstanding shares; your buy changed those shares and the function now implies $0.65.

Which pricing rules produce those marginal-price jumps: bonding curves and LMSR

Two common families of AMM pricing rules used in prediction markets are simple bonding curves and the Logarithmic Market Scoring Rule (LMSR).

• Simple bonding curves

  • Bonding curves map an outcome’s outstanding shares to a price. A common variant increases price as more shares of that outcome are bought. The curve includes a liquidity parameter (often called b or k) that controls how quickly price rises. Low liquidity → big jumps for small buys; high liquidity → small moves but more capital effectively locked as depth.

• Logarithmic Market Scoring Rule (LMSR)

  • LMSR defines a cost function C(q) that grows with the vector q of outstanding shares for each outcome. The marginal price for an outcome equals ∂C/∂q for that outcome. LMSR has a single parameter b that controls the market maker’s worst-case loss and therefore the depth: higher b = more liquidity and smaller price impact.

Both approaches share the same behavioral outcome: a trade increases the relevant q, the marginal price updates, and the next trader faces a different quote. In our worked example, any of these rules could produce the 3¢ move from $0.62 to $0.65 depending on the chosen parameter; the difference between rules is how cost grows and how worst-case loss or capital requirements scale.

How liquidity choices and trade-offs affect what you see day to day

Designing an AMM forces trade-offs you will observe in the market.

• Predictable availability vs. price slippage

  • Pro: You can always buy or sell at a known rule-based price.
  • Con: Large orders move the price against you in a predictable way. That is the cost of immediate execution—your $0.62 purchase bumped the price to $0.65.

• Liquidity requires capital or fees

  • To keep price moves small, the AMM needs a high liquidity parameter, which often means the platform or liquidity providers must lock capital or accept greater potential losses. Those costs show up as wider effective spreads or explicit fees.

• Transparency and manipulability

  • AMMs are transparent: the curve and parameters are public. That reduces information asymmetry but makes it obvious how much it costs to move a price, which can invite strategic trades around low-liquidity events.

• Price consistency across markets

  • Market-scoring rules like LMSR handle multiple outcomes and combinatorial events more naturally than naive bonding curves, but they still require careful parameter choice to keep linked prices sensible.

A common mistake is treating AMM prices as if they were free of trade cost. The observable market price includes the implied cost to move the market; if you want a tight probability estimate, look at small trade prices or markets with high liquidity.

If you need always-on pricing, are comfortable with predictable slippage, and prefer transparent rules, an AMM is a good match. If you want minimal price impact for large block trades and can wait for counterparties, an order-book market with committed liquidity providers may fit better. If you care about multi-outcome or combinatorial consistency, look for markets using LMSR or related scoring rules.

Further reading

• What Are Prediction Markets?
• How Do Prediction Markets Work?
• What Are Yes/No Contracts?