Case Study 1: Cross-Platform Price Discrepancies

Overview

When the same event is traded on multiple prediction market platforms, the prices often differ — sometimes by a significant margin. In efficient financial markets, such discrepancies are quickly eliminated by arbitrageurs. But in prediction markets, persistent price differences are the norm rather than the exception.

This case study examines real-world price discrepancies across platforms, investigates why they occur, and evaluates whether they represent genuine arbitrage opportunities.

The Scenario

It is November 2024, one week before the U.S. presidential election. The question "Will the Republican candidate win the 2024 presidential election?" is being traded on multiple platforms simultaneously:

The spread between the highest (Polymarket, 62%) and lowest (Metaculus, 55%) is a full 7 percentage points. Between the two real-money trading platforms (Polymarket and Kalshi), the gap is 5 percentage points.

Part 1: Understanding the Discrepancy

Question 1.1: Source of Differences

For each pair of platforms below, hypothesize the most likely reasons for the price difference:

Polymarket (62%) vs. Kalshi (57%)

Consider: - Geographic composition of traders: Polymarket is global (excluding U.S. officially); Kalshi is U.S.-only. Different populations may have different beliefs. - Crypto selection bias: Polymarket users must hold cryptocurrency. Does the crypto community have a systematic political bias? - Liquidity and market depth: How does each platform's liquidity affect price accuracy? - Position limits: Kalshi has individual position limits; Polymarket does not. How might this affect prices?

PredictIt (60%) vs. Kalshi (57%)

Consider: - Fee structure: PredictIt's 10% profit fee and 5% withdrawal fee create a "fee-adjusted" price that differs from the raw price. Adjust PredictIt's 60% for fees: if you buy at $0.60 and win, your net profit after 10% profit fee is $0.36, and after 5% withdrawal you receive $0.91. What is the "true" probability implied by a willing buyer at $0.60 on PredictIt? - The 850-trader limit: If the market is full, trapped informed traders cannot correct mispricing.

Manifold (59%) vs. Metaculus (55%)

Consider: - Market mechanism: Manifold uses an AMM; Metaculus uses forecast aggregation. How might these mechanisms respond differently to the same information? - Incentive structures: Manifold users bet play money; Metaculus users aim for calibration. Which incentive structure is more likely to produce accurate probabilities? - Selection bias in participants: Do Manifold and Metaculus attract different types of forecasters?

Question 1.2: Fee-Adjusted Prices

To make a fair comparison, we need to adjust prices for fees. Calculate the "break-even" true probability — the actual probability at which a rational trader would be indifferent between buying and not buying — for a Yes contract at the listed price on each platform.

Template for fee-adjusted break-even:

If you buy Yes at price $p$ on a platform with profit fee $f_p$ and withdrawal fee $f_w$:

• Cost: $p$ per contract
• Gross profit if Yes: $1 - p$
• Net profit after profit fee: $(1 - p)(1 - f_p)$
• Net after withdrawal fee: the entire payout $[p + (1-p)(1-f_p)]$ is reduced by $f_w$

You are indifferent when: $\text{Expected value} = 0$

$$q \cdot [(1-p)(1-f_p)] - (1-q) \cdot p = 0$$

where $q$ is the true probability. Solving:

$$q = \frac{p}{p + (1-p)(1-f_p)}$$

Calculate $q$ for:

1. Polymarket: $p = 0.62$, $f_p = 0$, $f_w \approx 0$ (minimal gas fees)
2. Kalshi: $p = 0.57$, $f_p = 0$, trading fee ~$0.01 per side
3. PredictIt: $p = 0.60$, $f_p = 0.10$, $f_w = 0.05$

Part 2: Is This Arbitrage?

Question 2.1: Classical Arbitrage

In traditional finance, arbitrage means riskless profit. To arbitrage the Polymarket/Kalshi gap:

1. Buy Yes on Kalshi at $0.57
2. Buy No on Polymarket at $0.38

Total cost: $0.57 + $0.38 = $0.95. Regardless of the outcome, one contract pays $1.00. Gross profit: $0.05 per pair.

Is this truly riskless? List all the risks and frictions:

• Can a single person legally trade on both Polymarket (non-U.S.) and Kalshi (U.S. only)?
• How do you fund both accounts simultaneously?
• What is the time value of capital locked in both positions?
• What are the actual transaction costs on each side?
• What happens if one platform resolves differently than the other?
• Is there currency risk (USD vs. USDC)?

Question 2.2: The Limits to Arbitrage

Even if the math works, explain why rational traders may not exploit this opportunity. Consider the framework of "limits to arbitrage" from behavioral finance:

1. Implementation costs: What does it actually cost to execute this trade?
2. Model risk: What if the two platforms use different resolution criteria?
3. Capital requirements: How much capital is tied up and for how long?
4. Legal risk: What legal exposure does a cross-platform arbitrageur face?
5. Fundamental risk: Is this even the same bet on both platforms?

Question 2.3: Synthetic Arbitrage

Even within a single platform, "arbitrage" can exist when related markets are mispriced relative to each other. For example, if Polymarket has:

• "Republican wins presidency" at 62%
• "Republican wins popular vote" at 45%
• "Republican wins presidency but loses popular vote" at 22%

Check: Is this set of prices internally consistent? If a Republican wins the presidency, they either won or lost the popular vote, so:

$$P(\text{Rep wins pres}) = P(\text{Rep wins pres and popular vote}) + P(\text{Rep wins pres but loses popular vote})$$

Does $0.62 = (0.45 \times k) + 0.22$ hold for some reasonable value? Note that winning the popular vote does not guarantee winning the presidency, so we need:

$$P(\text{Rep wins pres}) \leq P(\text{Rep wins popular vote and pres}) + P(\text{Rep wins pres, loses popular vote})$$

Check if the prices are consistent and discuss.

Part 3: Data Collection and Analysis

Question 3.1: Building a Cross-Platform Monitor

Using the Python code from this chapter's examples, write a script that:

1. Searches for similar markets on Polymarket, Manifold, and Metaculus.
2. Identifies pairs of markets that are likely about the same underlying event.
3. Computes the probability difference for each pair.
4. Flags pairs with differences greater than 5 percentage points.

Use the find_similar_markets function from example-03-multi-platform-dashboard.py as a starting point.

Question 3.2: Historical Analysis

If you have access to historical data (available through various APIs and data exports):

1. Collect historical prices for 10 events that were traded on both Polymarket and at least one other platform.
2. Track the price difference over the lifetime of each market.
3. Answer: Do price differences tend to converge as the event approaches? Or do they persist until resolution?
4. Plot the average absolute price difference as a function of time-to-resolution.

Question 3.3: Statistical Significance

For a set of cross-platform price pairs:

1. Run a paired t-test to determine if one platform systematically prices higher than another.
2. Compute the mean difference and 95% confidence interval.
3. If one platform is systematically higher, what does this imply about the biases of its user base?

Part 4: Explaining Persistent Discrepancies

Question 4.1: Market Segmentation Theory

Develop a theoretical framework explaining why prediction market prices diverge across platforms. Your framework should incorporate:

1. Participant heterogeneity: Different platforms attract different types of participants with different information and biases.
2. Friction barriers: The costs and difficulties of moving capital between platforms.
3. Regulatory segmentation: Legal restrictions that prevent cross-platform trading.
4. Informational asymmetry: Some platforms may have users with better access to certain types of information.

Question 4.2: When Discrepancies Are Informative

Sometimes the discrepancy itself contains useful information. Discuss:

1. If crypto-native users on Polymarket consistently price a technology event higher than Kalshi users, should we trust one platform more? Why?
2. If Metaculus forecasters (with no money at stake) give a lower probability than Polymarket traders (with real money at stake), which should we believe?
3. Could you build a "meta-forecast" by combining probabilities from multiple platforms? How would you weight each platform's contribution?

Part 5: Synthesis

Final Analysis

Write a 500-word analysis answering: Are cross-platform price discrepancies in prediction markets evidence of market inefficiency, or are they the rational result of market segmentation?

Your analysis should: - Define what "efficiency" means in the context of prediction markets - Distinguish between discrepancies that could theoretically be arbitraged and those that cannot - Propose a test that could distinguish between the "inefficiency" and "segmentation" hypotheses - Discuss implications for users who want to find the "best" probability estimate for a given event

Key Takeaways

1. Price discrepancies across prediction market platforms are common, persistent, and often significant (5-10 percentage points).
2. Fee structures, geographic restrictions, and regulatory constraints create natural barriers to arbitrage.
3. Different user bases bring different information and biases, which can lead to genuine differences in informed opinion.
4. Cross-platform comparison is valuable: no single platform's price should be taken as ground truth.
5. A sophisticated user should monitor multiple platforms and understand the biases inherent in each one.

End of Case Study 1