Arbitrage in Decentralized Prediction Markets

Updated 8 August 2025

Arbitrage dynamics in decentralized prediction markets are mechanisms where mispriced outcome probabilities create systematic profit opportunities by violating the unity constraint.
The interaction of second-order price dynamics and agent heterogeneity sustains cyclical mispricings, as traders exploit both intra- and inter-market inconsistencies.
Empirical evidence from platforms like Polymarket shows that arbitrage not only corrects price anomalies but also underscores the critical role of market design and transaction cost thresholds.

Decentralized prediction markets are mechanisms in which participants trade outcome-contingent claims, with market-clearing prices intended to reveal aggregated probabilistic beliefs about future events. Arbitrage dynamics in such markets arise whenever prices are inconsistent—with logical relationships, with exogenous information, or with rational updating—enabling certain agents to profit systematically by exploiting these inconsistencies. The research literature demonstrates that arbitrage opportunities may be durable or temporary depending on market microstructure, participant heterogeneity, design of outcome spaces, transaction costs, and underlying information flows. This article synthesizes theoretical and empirical results on the creation, sustainability, and impact of arbitrage in decentralized prediction markets, with attention to conditions sustaining perpetual arbitrage, the microstructure of mispricing, the effects of transaction costs, and the roles of market design and heterogeneity.

1. Mathematical and Structural Foundations

Prediction markets embody claims tied to an outcome space $\Omega = \{C_1,\ldots,C_n\}$ , typically structured to be exhaustive and mutually exclusive; i.e., precisely one event will occur. Let $v(Y_i,t)$ denote the market price of a "YES" (long) token for $C_i$ at time $t$ . In an ideal market, the constraint

$\sum_{i=1}^n v(Y_i, t) = 1$

should always hold, reflecting that the sum of probabilities across all outcomes is unity. Any deviation from this condition creates direct, riskless arbitrage opportunities, enabling a trader to purchase (when the sum $<1$ ) or sell (when the sum $>1$ ) a set of tokens guaranteeing a payout of $1$ with cost less (or more) than $1$, capturing profit equal to the discrepancy (Saguillo et al., 5 Aug 2025).

Deviation from this constraint, both within single markets (market rebalancing arbitrage) and across logically related but separately listed markets (combinatorial arbitrage), underpins much of the observed arbitrage activity in real-world decentralized prediction platforms such as Polymarket (Saguillo et al., 5 Aug 2025).

2. Mechanisms and Persistence of Arbitrage

2.1 Second-Order Price Dynamics

Standard price adjustment models posit first-order dynamics ( $dp/dt = \kappa\, \xi(p)$ , with $\xi(p)$ as excess demand). However, the presence of heterogeneous agents—some active arbitrageurs, others heuristic followers—naturally produces higher-order dynamics (Kemp-Benedict, 2012): $f_b \nu\, \Delta^2\bar{p}_t = f_a \mu\, \xi(\bar{p}_{t-1}) - (1 - f_b \nu)\, \Delta\bar{p}_t$ where $f_a$ and $f_b$ are agent group weights, $\nu$ models lagged reaction, and $\Delta^2\bar{p}_t$ is the second difference of prices. This structure allows persistent oscillations—or limit cycles—around equilibrium, with ongoing arbitrage opportunities even as damping terms seek to drive convergence. The core mechanism is the interplay between "conservative" demand components (gradient-driven, tending toward equilibrium) and divergence-free ("curl") components (non-conservative, sustaining cycles). Arbitrageurs systematically profit from misalignments induced by heuristic agents, with the market never fully settling (Kemp-Benedict, 2012).

2.2 Binary and Fractional Market Structures

Fractional binary markets, which discretize the fractional Black–Scholes model, admit explicit arbitrage opportunities in the absence of frictions, especially as the underlying process exhibits long-range dependence (Cordero et al., 2014). Introduction of transaction costs $\lambda$ modifies the arbitrage landscape, with critical cost thresholds $\lambda_c^{(N)}$ dictating when arbitrage is eliminated. However, $\lim_{N\to\infty} \lambda_c^{(N)} = 1$ : as markets are refined, arbitrage persists unless transaction costs are nearly total, even though in the continuous limit, arbitrage vanishes for any $\lambda>0$ . This robustness of arbitrage in discrete implementations has practical implications for real-world prediction markets that operate with transaction fees, indicating that "small" costs may not suffice to suppress arbitrage unless structurally high (Cordero et al., 2014).

3. Realized Arbitrage and Empirical Observations

Empirical on-chain data confirm that arbitrage is not merely theoretical. In an extensive audit of Polymarket order books (Saguillo et al., 5 Aug 2025), two forms of arbitrage were observed:

Arbitrage Type	Description	Executed Profits (Est.)
Market Rebalancing	Intramarket violations of $\sum v(Y_i,t) = 1$	Large-frequency, major
Combinatorial Arbitrage	Intermarket mispricings across dependent markets	Less frequent, focused

The exploitation of these opportunities resulted in an estimated $40$ million in arbitrage profits over the observed period. Detection required heuristic filtering due to the $O(2^{n+m})$ combinatorial explosion in condition comparisons, with LLMs used for efficient logic across markets (Saguillo et al., 5 Aug 2025).

The correction function of arbitrage is empirically significant: arbitrageurs' trades "rebalance" market prices toward probabilistic consistency, thereby restoring informational efficiency even in the absence of centralized surveillance.

4. Agent Heterogeneity and Market Microstructure

The sustainability of arbitrage is strongly linked to participant diversity. Models incorporating "active" arbitrageurs and "heuristic" followers (with lagged or biased responses) generate persistent mispricings (Kemp-Benedict, 2012). Second-order price dynamics (i.e., presence of $\frac{d^2p}{dt^2}$ terms) arise from this heterogeneity and can be decomposed via the Helmholtz–Hodge theorem into potential (conservative) and divergence-free (non-conservative) components: $\xi(p) = -\nabla\phi(p) + A(p)$ where $A(p)$ represents the curl-like, arbitrage-sustaining flow. In this framework, energy injected into cyclic price fluctuations via $A(p)$ offsets dissipative damping, perpetuating arbitrage and precluding strict equilibrium. Arbitrageurs’ profits are directly linked to the amplitude of price cycling and the response lag in the heuristics-driven majority.

5. Arbitrage, Market Design, and Efficiency

5.1 Impact on Market Efficiency

Arbitrage, particularly when systemic, forces the market probability vector toward logical coherence. Its presence both corrects mispricings and, when persistent, indicates inefficiency in market clearing or information aggregation. The observed phenomena reinforce the paradox that while arbitrage is a symptom of inefficiency, it is also a mechanism for restoring efficiency (Saguillo et al., 5 Aug 2025).

5.2 Implications for Platform and Mechanism Design

Empirical findings—especially the documented frequency and profitability of arbitrage—imply that platform design (structuring mutually exclusive/exhaustive conditions, semantic clarity, prompt resolution) is crucial for minimizing mispricings that allow arbitrageurs to extract excess returns (Saguillo et al., 5 Aug 2025). Automated semantic analysis and condition verification, as well as robust transaction fee structures calibrated above critical thresholds identified in theoretical models (Cordero et al., 2014), are among the strategies proposed to reduce vulnerability.

Additionally, mechanism design must balance the correction function of arbitrage against the risk of exploitative behavior (especially by bots or high-frequency participants). Enhancing resolution logic (via the use of trusted arbiters or well-designed outcome determination protocols) and improving cross-market dependency identification are also recommended.

6. Future Considerations and Open Issues

Several open questions and challenges remain. The scalability of arbitrage detection and mitigation (especially as the number of markets/conditions grows) is nontrivial, and empirical work emphasizes the utility of LLMs but also the necessity of expert curation for robust logic inference (Saguillo et al., 5 Aug 2025). The question of how persistent arbitrage affects long-run market integrity, how it interacts with sophisticated trading strategies, and what unanticipated consequences may stem from its attempted suppression remain areas for ongoing theoretical and applied research.

Attention must also be paid to the possible evolutionary adaptation of markets—mechanisms or agents can self-adjust to eliminate certain arbitrage opportunities over time, but may be slow or incomplete, leaving windows of profit. Understanding this dynamic interaction, especially in markets that are not maximally liquid or where agents have substantial computational asymmetries, is essential for both market designers and active participants.

Arbitrage in decentralized prediction markets is thus both a structural inevitability and a key dynamic for price discovery and efficiency. Mathematical characterizations, empirical observations, and technological advances in semantic analysis and agent modeling together elucidate the mechanisms, limitations, and applications of arbitrage, informing both theory and platform engineering in the evolving landscape of decentralized finance.