Unravelling the Probabilistic Forest: Arbitrage in Prediction Markets

2025-08-05

AI Summary

This study empirically investigates systematic arbitrage opportunities in the Polymarket prediction market. It addresses three core questions: (Q1) conditions under which arbitrage arises; (Q2) whether arbitrage behavior is empirically observed; and (Q3) whether such opportunities are effectively exploited. Methodologically, we introduce two novel arbitrage classes—market rebalancing arbitrage and combinatorial arbitrage—and design a heuristic pruning strategy grounded in timeliness, thematic similarity, and logical composition to enhance scalability in cross-market relational analysis. Leveraging on-chain historical order-book data, we combine heuristic filtering with expert validation to efficiently identify arbitrageable market states at scale. Our findings reveal significant pricing inconsistencies in Polymarket: users have successfully captured approximately $40 million in arbitrage profits, providing robust empirical evidence of its systemic inefficiency.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Multiagent Systems: Mechanism Design
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Polymarket is a prediction market platform where users can speculate on future events by trading shares tied to specific outcomes, known as conditions. Each market is associated with a set of one or more such conditions. To ensure proper market resolution, the condition set must be exhaustive -- collectively accounting for all possible outcomes -- and mutually exclusive -- only one condition may resolve as true. Thus, the collective prices of all related outcomes should be $1, representing a combined probability of 1 of any outcome. Despite this design, Polymarket exhibits cases where dependent assets are mispriced, allowing for purchasing (or selling) a certain outcome for less than (or more than) $1, guaranteeing profit. This phenomenon, known as arbitrage, could enable sophisticated participants to exploit such inconsistencies. In this paper, we conduct an empirical arbitrage analysis on Polymarket data to answer three key questions: (Q1) What conditions give rise to arbitrage (Q2) Does arbitrage actually occur on Polymarket and (Q3) Has anyone exploited these opportunities. A major challenge in analyzing arbitrage between related markets lies in the scalability of comparisons across a large number of markets and conditions, with a naive analysis requiring $O(2^{n+m})$ comparisons. To overcome this, we employ a heuristic-driven reduction strategy based on timeliness, topical similarity, and combinatorial relationships, further validated by expert input. Our study reveals two distinct forms of arbitrage on Polymarket: Market Rebalancing Arbitrage, which occurs within a single market or condition, and Combinatorial Arbitrage, which spans across multiple markets. We use on-chain historical order book data to analyze when these types of arbitrage opportunities have existed, and when they have been executed by users. We find a realized estimate of 40 million USD of profit extracted.

Problem

• Identify conditions causing arbitrage in Polymarket prediction markets
• Analyze occurrence and exploitation of arbitrage opportunities in Polymarket
• Develop scalable method to detect arbitrage across multiple markets

Innovation

• Heuristic-driven reduction for scalable arbitrage analysis
• On-chain historical order book data analysis
• Market Rebalancing and Combinatorial Arbitrage identification