The Evolution of Pricing Mechanisms in Prediction Markets: From AMM to Order Book

A prediction market is essentially a trading venue for the probability of future events. Users can express their judgment on a specific event by purchasing an option.

Due to the differences in trading probability events compared to common asset trading, the pricing and liquidity mechanisms of prediction markets have their unique characteristics. Taking a well-known prediction market platform as an example, its pricing mechanism has undergone significant changes from the beginning to now, initially adopting an automated market maker mechanism known as the logarithmic market scoring rule (LMSR), and now upgraded to an off-chain order book model.

Understanding the characteristics of LMSR can help us understand the early pricing mechanism of the platform, as well as the considerations of other protocols that adopt LMSR, and it can also explain the reasons why the platform ultimately shifted to an order book.

Characteristics and Advantages/Disadvantages of LMSR

LMSR is a pricing mechanism designed for prediction markets that allows users to buy shares of a certain option based on their judgment, and the market automatically adjusts prices according to total demand. The most significant feature of LMSR is that it can complete transactions without relying on a counterparty; even the first trader can have the system price a transaction. This gives prediction markets a "perpetual liquidity" similar to that of some decentralized exchanges.

The LMSR is essentially a cost function model that calculates prices based on the "shares" currently held for each option. This mechanism ensures that prices reflect the market's expected probabilities for different event outcomes.

The core formula of LMSR is:

C(q) = b * ln(Σe^(qi/b))

Where C is the cost function, b is the liquidity parameter, and qi is the current purchased share of the i-th option.

The most important feature of LMSR is that the sum of the prices of all outcomes is always equal to 1. When a user purchases a certain option, the price of that option increases, while the prices of other options decrease, maintaining the total sum at 1.

The price in LMSR is the marginal derivative of the cost function, which means the marginal cost that needs to be paid when buying one more unit of a certain option. This implies that the larger the purchase quantity of a certain option, the higher the price will gradually rise, and ultimately the price will tend to reflect the market's subjective probability of each option occurring.

The size of the liquidity parameter b determines the smoothness of the price curve, which is the liquidity or "thickness" of the market. The larger the value of b, the smoother the curve, allowing the market to absorb larger trading volumes without causing significant price fluctuations.

The Mechanism Trade-offs and Paradigm Shifts of LMSR

The fundamental design goal of LMSR is information aggregation, rather than market maker profit. It addresses the liquidity supply problem in prediction markets when there is a lack of counterparties in the early stages.

The advantage of LMSR lies in providing unconditional liquidity and controllable market-making risks. It ensures that there are counterparties available for trading at any point in time. At the same time, the maximum loss for market makers is predictable and bounded, determined jointly by b and the number of market outcomes n.

However, LMSR also has inherent flaws:

1. The b parameter dilemma leads to static liquidity: The b value is usually set when the market is created and cannot be adjusted adaptively according to actual conditions.

2. Market makers play a subsidizing role: The theoretical mathematical expectation of the LMSR model is a loss, which is not suitable for profit-seeking market maker models.

3. High Gas costs when implemented on-chain: The logarithmic and exponential operations involved in LMSR consume more Gas than common arithmetic operations.

These factors led some platforms to ultimately abandon LMSR in favor of an order book model. This shift is based on the following considerations:

1. Improve capital efficiency: The order book allows liquidity to be concentrated in the most active price ranges.

2. Optimize trading experience: A mature order book market can provide lower slippage in trade execution.

3. Attract professional liquidity: The order book is the market model that professional traders are most familiar with.

Pricing and Liquidity Mechanisms of Current Mainstream Prediction Markets

Currently, mainstream prediction market platforms adopt a hybrid model of on-chain settlement and off-chain order books:

• Off-chain order book: Users' limit orders are submitted and matched off-chain, with instant operations and no Gas costs.
• On-chain settlement: After the order is successfully matched, the final asset delivery is executed on-chain through a smart contract.

This model ensures the finality of trading results while maintaining the flexibility of the order book.

In terms of price anchoring, a mechanism of share-based minting and arbitrage cycles has been adopted:

1. The core foundation is the minting and redemption of complete shares, establishing the value peg of "1 YES share + 1 NO share = $1".

2. YES shares and NO shares trade freely as independent assets on their respective order books.

3. Arbitrageurs ensure that the sum of the prices of YES and NO shares always converges to $1 through "minting-selling" or "buying-redeeming" operations.

This mechanism uses the profit-seeking behavior of market participants to maintain the stability of system prices.

The Possibility of Combining Prediction Markets with Decentralized Exchanges

As the user base of prediction markets grows, the potential for its integration with decentralized exchanges (DEX) is becoming increasingly apparent:

1. Provide native risk hedging tools for the DEX ecosystem: The event contracts of the prediction market can be directly used to hedge the on-chain position risks of DEX users.

2. As a leading indicator for centralized liquidity management in DEX: The real-time odds of the prediction market can be used to dynamically adjust the LP position range in the DEX.

3. Foster the emergence of new structured financial products: Link DEX core indicators with prediction market event outcomes to design conditional yield distribution models.

The prediction market is evolving into the "risk pricing layer" and "information oracle" of the cryptocurrency industry. Its deep integration with foundational protocols such as DEX will be a key factor in driving the DeFi ecosystem towards greater efficiency, maturity, and resilience.