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Manipulation in Prediction Markets: An Agent-based Modeling Experiment

This paper employs agent-based modeling and theoretical analysis to demonstrate that while prediction markets generally exhibit self-regulatory stability, high-budget "whale" agents can temporarily distort prices, with the magnitude and duration of such manipulation significantly amplified by the herding behavior and slow learning rates of other market participants.

Original authors: Bridget Smart, Ebba Mark, Anne Bastian, Josefina Waugh

Published 2026-01-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bridget Smart, Ebba Mark, Anne Bastian, Josefina Waugh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a giant, digital town square where people bet money on whether a specific event will happen—like "Will Candidate X win the election?" In this square, the price of a bet acts like a crowd-sourced weather forecast: if the price is high, the crowd thinks the event is likely; if it's low, they think it's unlikely.

This paper, titled "Manipulation in Prediction Markets: An Agent-based Modeling Experiment," asks a scary question: What happens when a very rich person (a "Whale") enters this town square and tries to trick everyone into believing a lie?

Here is a simple breakdown of what the researchers did and found, using everyday analogies.

1. The Setup: A Digital Betting Pool

The researchers built a computer simulation (a "virtual world") to mimic these betting markets.

The Players: They created 100 virtual people (agents). Some are "experts" who have good information, and some are just guessing.
The Rules: Everyone has a different amount of money (budget) and different levels of stubbornness. Some people change their minds easily when they see new info; others are stubborn and stick to their guns.
The Goal: The market tries to figure out the "true" outcome of an election. In a perfect world, the betting price should match the actual result.

2. The Villain: The "Whale"

In the financial world, a "Whale" is a participant with so much money that their actions can move the whole ocean.

The Experiment: The researchers introduced one "Whale" into their simulation. This Whale had a massive budget and a biased opinion (they were convinced the wrong candidate would win).
The Strategy: The Whale started buying and selling aggressively to push the price toward their false belief, hoping to trick the other 99 people.

3. The Findings: Can the Whale Win?

The researchers ran thousands of simulations to see what happened. Here is what they discovered:

A. The Market is Usually Tough (Self-Correcting)

If the Whale tries to push the price too hard, the other smart bettors usually notice. They see the price is "wrong" compared to the real information they have, so they bet against the Whale.

Analogy: Imagine the Whale is a giant trying to push a heavy boulder up a hill. The other 99 people are like a team of hikers pushing it back down. Usually, the hikers win, and the boulder (the price) stays where it belongs.
Result: The market is resilient. It can correct itself quickly unless the Whale has an enormous amount of money (about 40% of the total money in the pool).

B. The "Stubborn" and "Sheep" Problem

The market only stays broken if the other people make specific mistakes:

The Sheep (Herding): If the other bettors stop thinking for themselves and just follow the crowd price (like sheep following a leader), the Whale's fake price sticks around longer.
The Stubborn: If the other bettors are too stubborn to update their beliefs when they see new information, the Whale's lie lasts longer.
Analogy: If the hikers are too stubborn to listen to the truth, or if they are too scared to push back and just follow the giant, the boulder stays at the top of the hill.

C. The Profit Paradox

Interestingly, the researchers found that when a Whale messes up the price, it actually creates a profit opportunity for the smart, well-informed bettors.

Analogy: If the Whale pushes the price up to $10 for something worth $5, the smart bettors can sell their shares at $10 and make a quick profit before the market corrects itself. The Whale's manipulation hurts the market's accuracy, but it makes money for the smart traders who spot the error.

4. The Big Picture: Why Should We Care?

The paper concludes that while prediction markets are generally good at predicting the future, they are vulnerable to manipulation if the rules allow one person to hold too much money.

The Danger: If a wealthy person can push the price to look like a different candidate is winning, it might trick real voters, news outlets, or politicians into thinking that candidate is ahead. This could change how people vote or how campaigns spend money.
The Solution: The authors suggest that to keep these markets honest, there should be limits on how much one person can bet. In the past, markets had strict limits (like $3,500 per person), which kept Whales out. Newer markets allow millions of dollars per bet, which opens the door for manipulation.

Summary

Think of a prediction market as a crowd-sourced truth machine.

Normally: It works great because everyone's different opinions cancel out the noise.
With a Whale: A rich person can temporarily jam the machine with a false signal.
The Fix: The machine only stays jammed if the crowd is too lazy (herding) or too stubborn to correct the error. To prevent this, we need rules that stop one person from having too much power over the whole machine.

The paper does not claim that this manipulation definitely changes election results in the real world yet, but it warns that the potential is there if we don't set limits on how much money one person can throw into the mix.

Technical Summary: Manipulation in Prediction Markets: An Agent-based Modeling Experiment

Problem Statement
Prediction markets aggregate dispersed beliefs to forecast binary event outcomes, often demonstrating high accuracy in political elections. However, the rapid expansion of these markets—exemplified by platforms like Kalshi and Polymarket allowing multi-million dollar positions—has raised concerns regarding their susceptibility to manipulation. Unlike earlier markets with strict per-trader position limits (e.g., Iowa Electronic Markets, PredictIt), modern platforms permit "whales" (high-budget agents) to control significant capital. The central problem addressed is whether these markets function as self-correcting information mechanisms or if they can sustain price deviations introduced by a highly resourced, biased minority. Specifically, the authors investigate under what conditions such distortions persist and how they interact with other market participants' behaviors, such as herding and stubbornness.

Methodology
The authors develop an open-source Agent-Based Model (ABM) to simulate a prediction market over discrete time steps. The model features:

Agents: $N$ betting agents with heterogeneous attributes, including expertise ( $e_i$ ), bias ( $b_i$ ), risk aversion ( $r_i$ ), stubbornness ( $s_i$ ), and initial budgets ( $B_{i,0}$ ).
Information Structure: Agents receive a "fuzzy" private signal of the true election outcome ( $\eta_t$ ), modeled as a random walk. The signal's variance is inversely related to the agent's expertise.
Valuation and Learning: Agents update their internal valuations ( $V_{i,t}$ ) based on private signals and, optionally, a herding parameter ( $h_i$ ) that weights the current market price. Stubbornness ( $s_i$ ) governs the rate at which agents incorporate new information.
Market Mechanism: A central market matches buy/sell orders via random double-auction rules. The market price ( $m_t$ ) updates based on net demand, scaled by a parameter $\lambda$ .
Simulation Protocol: The study first validates the model's stability across a broad parameter space. It then introduces a single "whale" agent with a fixed biased valuation and a specific proportion of total market capital ( $\rho_w$ ) to test for price distortion.
Theoretical Analysis: Complementing the simulations, the authors derive a theoretical solution for the steady-state price error, linearizing order sizes to analyze the interaction between whale budget share, bias, and the decay of errors in the presence of herding.

Key Contributions

Open-Source Framework: The authors provide an open-source ABM and a Dash application with a graphical user interface, allowing for the exploration of agent behavior, parameter variation, and information shocks.
Systematic Analysis of Manipulation: The study isolates the effects of concentrated capital ("whales") on market accuracy, moving beyond theoretical assumptions of small traders to model realistic capital concentrations.
Integration of Behavioral Dynamics: The model explicitly incorporates heterogeneous expertise, learning rates, and herding behavior to determine how these factors influence market resilience against manipulation.
Theoretical Corroboration: The paper derives analytical relationships showing that steady-state price errors scale linearly with the whale's budget share and misvaluation, and that the decay of these errors depends on the learning dynamics and herding intensity of non-whale agents.

Results

Market Stability: In the absence of whales, the prediction market exhibits robust stability and accuracy across a wide range of parameter values. The market price closely tracks the true election outcome, with mean squared errors (MSE) comparable to leading election forecasting models.
Whale Impact: Whales can temporarily distort market prices. The magnitude of the distortion is proportional to the product of the whale's budget share and their misvaluation. A whale requires approximately 40% of total market capital to induce meaningful, sustained error under the tested parameters.
Role of Herding and Stubbornness: The presence of herding behavior ( $h_i > 0$ $h_{i} > 0$ ) and high stubbornness ( $s_i \approx 1$ $s_{i} \approx 1$ ) among non-whale agents significantly impacts the recovery of the market.
- Moderate herding does not drastically alter recovery rates.
- High herding ( $h_i = 1$ ) combined with high stubbornness can lead to instability, characterized by oscillations in market price and a slower decay of price distortions.
Profit Opportunities: Temporary price distortions created by whales create profit opportunities for well-informed non-whale agents (those with high expertise), who can exploit the misaligned prices.
Theoretical Validation: The theoretical analysis confirms that the steady-state error ( $\delta_S$ ) equals the whale's budget fraction ( $\rho$ ) multiplied by the whale's valuation error ( $\Delta_S$ ). It further demonstrates that error decay is faster when agents have low stubbornness and low herding weights.

Significance and Claims
The paper claims to provide a cautionary framework for the regulation and design of prediction markets, particularly in election contexts where prices may serve as public information signals.

Regulatory Implications: The findings suggest that while prediction markets are generally resilient, they are vulnerable to manipulation when concentrated capital is allowed without constraints. The authors argue for a regulatory approach that balances recreational freedom with democratic integrity, potentially through restrictions on individual trade sizes or overall budget limits where enforceable.
Feedback Loops: The study highlights the risk of endogeneity: if manipulated market prices influence voter beliefs, campaign strategies, or media narratives, the distortion could feed back into the political process, potentially altering the very outcome being predicted.
Modesty of Claims: The authors explicitly state that they do not empirically validate the feedback loop between market prices and real-world election outcomes, noting that this remains an open question. Their contribution is primarily in characterizing the conditions under which market prices can be distorted and sustained, providing a basis for precautionary policy measures. They emphasize that their model isolates specific mechanisms (capital concentration, herding) rather than simulating the full complexity of real-world political ecosystems.