A prediction market is essentially an open market where participants forecast specific outcomes by trading on the likelihood of various events. These markets function similarly to a free-market economy, where market prices adjust based on the collective wisdom of the participants. Prediction markets allow users to trade on the probability of certain events, with the resulting market price reflecting the perceived likelihood of those outcomes.

According to the definition, prediction markets are “exchange-traded markets created for the purpose of trading the outcome of events. The market prices can indicate what the crowd thinks the probability of the event is.” While this definition captures the basic concept, prediction markets offer much more depth and complexity that warrants further exploration.

The openness of a prediction market is one of its most crucial features. Unlike traditional betting, where odds are set by bookmakers based on specific formulas, prediction markets start with even odds. As participants trade based on their knowledge and insights, the market naturally adjusts the prices to reflect the most likely outcomes.

To illustrate how prediction markets operate, consider a hypothetical example involving the FIFA World Cup Final in December 2022, potentially contested by Argentina and England. Based on the data available, centralized bookmakers might set the odds in Argentina’s favor, suggesting a 67% chance of Argentina winning and a 33% chance for England.

In contrast, a prediction market operates without a centralized bookmaker. Participants can create a market by posing a question like “Who will win the FIFA World Cup Final?” and list possible outcomes, such as “Argentina” or “England.” This setup is known as a binary prediction market.

In our example, two outcome tokens would be available:

• ARGWIN (Argentina Wins)

• ENGWIN (England Wins)

These tokens start at an even price, say 50/50. As participants purchase tokens based on their expectations, the prices will fluctuate according to supply and demand. If more people buy "ARGWIN," its price will increase, while "ENGWIN" will decrease. Over time, the market will self-regulate, with token prices reflecting the most likely outcome—possibly aligning with the bookmakers’ odds of 67/33.

Prediction markets thus enable accurate predictions without the need for dedicated forecasters or data analysts. The majority of participants will only engage in predictions if they have some insight or information about the likely outcome.

A prediction market can also be conceptualized as a derivative market. Since markets function as information processors, they can be designed within the framework of information theory, making prediction markets particularly adaptable to this model.

Prediction markets, also known as betting markets, information markets, decision markets, idea futures, or event derivatives, allow participants to trade contracts based on the outcomes of unknown future events. The market prices that emerge from these contracts can be seen as a collective prediction from market participants. If these contracts are tied to the price of certain assets, the prediction market effectively becomes a derivative market.

Advantages of Prediction Markets as Derivative Markets:

• No Need for an Underlying Asset: These markets do not require an underlying asset to function. An oracle that introduces information about the underlying asset and a currency for pledging are sufficient to establish such a market.

• Automated Market Makers (AMMs): It is relatively straightforward to implement an automated market maker for prediction markets. The study of prediction markets has been instrumental in developing AMM algorithms.

• Versatility: Prediction markets can offer general-purpose products by designing appropriate prediction events.

• Isomorphism with European Options: Prediction markets share an isomorphic relationship with European options, allowing the migration of pricing models from options to prediction markets.

• Capital Efficiency: Prediction markets are highly capital-efficient, often more so than traditional betting markets.

• No Short Squeeze: In prediction markets, the responsibility of participants is limited by their pledged assets, eliminating the risk of a short squeeze.

Disadvantages of Prediction Markets as Derivative Markets:

• Risk for Liquidity Providers: Liquidity providers hold positions and are exposed to high risks, particularly during black swan events. However, for risk-neutral investors, this may be acceptable.

• Novelty and Learning Curve: Prediction markets are a relatively new concept, and it may take time for participants to fully understand their mechanics. However, novelty is a common feature in the blockchain space.

• Unknown Risks: As with any new design, there may be undiscovered disadvantages.

Prediction markets are specialized financial markets where participants trade contracts based on the outcomes of future events, such as political elections, sports outcomes, or economic indicators. The prices of these contracts reflect the collective beliefs of the market participants about the likelihood of these events. Two primary mechanisms underpin the functioning of prediction markets: the Continuous Double Auction (CDA) and the Logarithmic Market Scoring Rule (LMSR). Each mechanism offers distinct advantages and faces specific challenges, particularly concerning liquidity and price accuracy. This article explores the intricacies of these mechanisms, their applications in prediction markets, and their relationship to automated market makers (AMMs).

The Continuous Double Auction (CDA) is one of the most common mechanisms used in financial markets, including prediction markets. In a CDA, traders interact directly with one another by placing buy (bid) and sell (ask) orders into an order book. The order book, a central feature of the CDA mechanism, lists all outstanding orders, with bids on one side and asks on the other. When a bid matches an ask, a trade occurs, and the transaction is executed at the matching price. The dynamics of the CDA mechanism can be illustrated using sigmoid functions for bids and asks. The sigmoid function, defined as:

$$\text{Bids}(P) = \frac{50}{1 + \exp(0.5 \times (P - 10))}$$

$$\text{Asks}(P) = \frac{50}{1 + \exp(-0.5 \times (P - 10))}$$

Here, PPP represents the price level. The bid function gradually decreases as the price increases, while the ask function increases, creating a natural equilibrium where the two curves intersect. This intersection represents the price at which trades occur. The sigmoid function models the gradual change in order quantity as prices move away from a central value.

A key characteristic of the CDA is its reliance on direct trader interactions to facilitate price discovery. Traders can place orders at any time, and these orders remain in the order book until they are matched by an opposing order. The flexibility of the CDA allows traders to set their desired prices, which can lead to efficient price discovery in markets with high liquidity. However, this same reliance on direct interactions can be a limitation in markets with fewer participants. In thin markets, where there are not enough traders to match orders quickly, the CDA can suffer from low liquidity, leading to wider spreads between the highest bid and the lowest ask. This can reduce the efficiency of the market and make it more difficult to arrive at accurate price predictions.

In the context of prediction markets, the CDA mechanism has been widely used due to its simplicity and its ability to facilitate straightforward trading. However, the challenges associated with low liquidity in prediction markets, where participant numbers can be limited, have led to the exploration of alternative mechanisms like the LMSR.

The Logarithmic Market Scoring Rule (LMSR) is an automated market maker (AMM) mechanism specifically designed to address the liquidity issues often encountered in prediction markets. Unlike the CDA, where trades occur directly between participants, the LMSR involves a central automated market maker that acts as the counterparty to all trades. This market maker continuously provides buy and sell quotes, calculated using a logarithmic scoring rule, which adjusts prices based on the total volume of outstanding contracts.

The LMSR mechanism can be modeled using a logarithmic function for price adjustments and a logistic function for liquidity. The logarithmic function for price adjustment is given by:

$$\text{Price}(T) = \log(T + 1) \times 10$$

Where TTT represents the number of trades. This function reflects how prices increase at a decreasing rate as more trades occur, preventing prices from becoming too extreme. The liquidity can be modeled using a logistic function:

$$\text{Liquidity}(T) = \frac{100}{1 + \exp(-0.1 \times (T - 25))}$$

This function shows how liquidity changes with the number of trades, peaking at a certain trade volume and then tapering off.

One of the significant advantages of the LMSR is its ability to provide constant liquidity, ensuring that traders can always execute a trade without needing to wait for a matching order from another participant. The LMSR accomplishes this by automatically adjusting prices as more contracts are bought or sold. This price adjustment is logarithmic, meaning that as the number of contracts favoring one outcome increases, the price for that outcome rises at a decreasing rate. This mechanism prevents prices from becoming too extreme, even in cases of heavy trading in one direction, thereby stabilizing the market.

The LMSR is particularly well-suited for prediction markets because it mitigates the risks associated with low liquidity. In markets where participant numbers are small, the LMSR ensures that trading can continue smoothly, and prices reflect the collective sentiment of the market, even with fewer active traders. However, this comes at the cost of potential losses for the market maker, as it might need to subsidize trades to maintain liquidity. Despite this, the LMSR's design ensures that these losses are capped, making it a sustainable mechanism for market owners.

Ken Kittlitz, the Chief Technology Officer at Consensus Point, has highlighted the practical benefits of using LMSR in prediction markets. He notes that the presence of an automated market maker "makes a huge difference to the success of the market," as it provides a steady stream of liquidity and simplifies the trading process for participants. By ensuring that buy and sell orders are always available at a wide range of prices, the LMSR makes the market more accessible and intuitive, which can lead to greater participation and, consequently, more accurate predictions.

While both CDA and LMSR mechanisms are used in prediction markets, they serve different purposes and are best suited to different market conditions. The CDA is effective in markets with high liquidity, where there are enough participants to ensure that buy and sell orders are regularly matched. In such environments, the CDA can facilitate efficient price discovery and allow the market to reflect the true collective belief of its participants. However, in markets with lower liquidity, the CDA's reliance on direct trader interactions can lead to inefficiencies, such as wider spreads and less accurate price predictions.

On the other hand, the LMSR shines in environments where liquidity is a concern. Its automated market-making feature ensures that trades can occur at any time, regardless of the number of participants. This constant provision of liquidity makes LMSR particularly valuable in prediction markets, where participation might be sporadic or limited. The LMSR's ability to adjust prices dynamically based on trading volume also helps stabilize the market and prevent extreme price fluctuations, which can be crucial in ensuring that the market's predictions remain reliable.

Automated market makers (AMMs) like LMSR play a crucial role in maintaining liquidity in markets that might otherwise suffer from low trading volume. In prediction markets, where the number of participants can vary significantly, the presence of an AMM ensures that the market remains functional and that prices continue to reflect the collective sentiment of traders.

AMMs operate by using algorithms to set prices and automatically offer trades. In the case of LMSR, this algorithm is based on a logarithmic function that adjusts prices as the volume of trades changes. This continuous adjustment helps prevent the market from becoming overly biased towards a particular outcome, ensuring that prices remain within a reasonable range. By providing this stabilizing force, AMMs like LMSR enable prediction markets to function effectively even in the absence of a large number of participants.

Prediction markets can take several forms, each suited to different scenarios:

1. Binary Markets: These involve two possible outcomes, such as "Yes" or "No." The FIFA World Cup example is a typical binary market.

2. Categorical Markets: Similar to binary markets but with more than two options. For instance, predicting the winner of a tournament where several teams are still in contention.

3. Scalar (Range) Markets: These predict outcomes within a specific range, such as the future price of an asset. Participants are rewarded based on how close their prediction is to the actual outcome.

4. Combinatorial Markets: The most complex form, where users combine multiple prediction markets to create forecasts of multifaceted outcomes.

In a Categorical Market, if we were to predict the winner of the FIFA World Cup after the quarter-finals with eight teams remaining, each outcome token might start at 0.125 ZTG. If you correctly predicted the winner early, you could make a significant profit once the market concludes.

In a Scalar Market, imagine predicting the price of the Polkadot token (DOT) by the end of Q3 2022. Participants could predict any price within a set range (e.g., $0 to $20), and their rewards would depend on how close their prediction was to the actual price.

Combinatorial prediction markets allow for more complex forecasting by combining several prediction markets. For example, predicting the success of a new iPhone launch could involve multiple variables like color options, included accessories, and pricing. By combining these factors, participants can generate more accurate predictions of the product’s success.

Combinatorial markets are particularly useful in scenarios like weather insurance, where multiple variables affect the outcome. A devoted article will explore the complexities of combinatorial prediction markets in more detail.

Prediction markets offer a unique advantage over traditional polling methods. Instead of relying on labor-intensive surveys, prediction markets leverage financial incentives to encourage accurate predictions. The market's natural dynamics ensure that overpriced shares are corrected by participants buying undervalued ones, leading to more reliable data.

Prediction markets are a powerful tool for forecasting a wide range of outcomes, from sports results and asset prices to political decisions and weather events. Those with valuable insights are incentivized to participate and correct any market imbalances, while less informed participants are naturally dissuaded from taking significant risks.

The goal of any prediction market platform should be to create a user-friendly environment that attracts liquidity and offers rapid response times, ensuring that prediction markets are easy to create and participate in. Decentralization and permissionless participation further enhance the platform’s potential, empowering users to uncover valuable data about the world around us. The Continuous Double Auction (CDA) and Logarithmic Market Scoring Rule (LMSR) are two distinct mechanisms that serve different needs in prediction markets. The CDA facilitates direct interactions between traders and is effective in markets with high liquidity, while the LMSR, as an automated market maker, ensures constant liquidity and stabilizes prices, making it ideal for markets with lower participation. Understanding the strengths and limitations of each mechanism is essential for designing effective prediction markets that can accurately aggregate information and produce reliable forecasts. As the field of prediction markets continues to evolve, the role of AMMs like LMSR will likely become increasingly important in ensuring the robustness and accuracy of market predictions.

Disclaimer: This post is for general informational purposes only and does not constitute investment advice, recommendations, or a solicitation to buy or sell any securities. It should not be used as the basis for making any investment decision and should not be relied upon for accounting, legal, tax advice, or investment recommendations. You are encouraged to consult your own advisers regarding legal, business, tax, or other related matters concerning any investment decisions. Certain information included here may have been obtained from third-party sources, including portfolio companies of funds managed by Aquarius. The opinions expressed in this post are those of the authors and do not necessarily reflect the views of Aquarius or its affiliates. These opinions are subject to change without notice and may not be updated.