Manipulation in Prediction Markets: An Agent-based Modeling Experiment

TL;DR

This paper analyzes the susceptibility of prediction markets to manipulation by a high-budget whale using an open-source agent-based model that simulates heterogeneous bettors, noisy signals, and learning dynamics. It demonstrates that a biased, well-funded agent can temporarily distort market prices, with the magnitude and duration scaling with the whale’s budget share and tempered by non-whale learning and herding behavior; a complementary theoretical analysis links these distortions to AR(2) dynamics and stability conditions. The work provides evidence that prediction markets can self-correct under typical conditions but remain vulnerable under concentrated wealth and strong social feedback, highlighting implications for market design and policy in election contexts. By offering an open-source ABM and a Dash-based interface, the authors enable further exploration of information shocks, network effects, and alternative market mechanisms, informing regulation and the interpretation of market-based election signals.

Abstract

Prediction markets mobilize financial incentives to forecast binary event outcomes through the aggregation of dispersed beliefs and heterogeneous information. Their growing popularity and demonstrated predictive accuracy in political elections have raised speculation and concern regarding their susceptibility to manipulation and the potential consequences for democratic processes. Using agent-based simulations combined with an analytic characterization of price dynamics, we study how high-budget agents can introduce price distortions in prediction markets. We explore the persistence and stability of these distortions in the presence of herding or stubborn agents, and analyze how agent expertise affects market-price variance. Firstly we propose an agent-based model of a prediction market in which bettors with heterogeneous expertise, noisy private information, variable learning rates and budgets observe the evolution of public opinion on a binary election outcome to inform their betting strategies in the market. The model exhibits stability across a broad parameter space, with complex agent behaviors and price interactions producing self-regulatory price discovery. Second, using this simulation framework, we investigate the conditions under which a highly resourced minority, or ''whale'' agent, with a biased valuation can distort the market price, and for how long. We find that biased whales can temporarily shift prices, with the magnitude and duration of distortion increasing when non-whale bettors exhibit herding behavior and slow learning. Our theoretical analysis corroborates these results, showing that whales can shift prices proportionally to their share of market capital, with distortion duration depending on non-whale learning rates and herding intensity.

Figures (7)

• Figure 1: Stylized representation of behavioral attributes and their effects on betting agent behavior. Panel (A) represents the buy-sell decision of an individual agent $i$ at time $t$ with budget $B_{i,t} = \$100$ whose internal market valuation $V_{i,t} = \$0.50$. Each line represents their buy-sell decision at various market prices $m_t$, varying their degree of risk aversion where $r_i \rightarrow 0$ implies higher levels of risk aversion. Panel (B) represents a high-expertise ($e_{i} = 0.9$) betting agent's learning process over 50 time steps. The agent starts the simulation with an internal valuation $V_{i,0} = \$0.10$ receiving a signal of the true value $\eta_t$ (a constant value in this stylized representation). Each line represents the learning trajectory mediated by varying stubbornness $s_i$. Panel (C) represents the distribution of signal $M_{i,t}$ where the true value $\eta_t = \$0.50$, varying expertise $e_i$ and bias $b_i$. Each color represents a different level of bias $b_i$ and each value on the x-axis represents a different level of expertise $e_i$. The gray sections represent the limits ([$0,$1]) of any market valuation.
• Figure 2: Panel A and C show a single simulation from the ABM. Panel A has the true election outcome (red), market price (black) alongside the net supply and demand indicating upward or downward pressure on the market price. The average market valuation of bettors is shown in purple. Panel C visualizes this single run through the number of contracts held across all agents (navy), as well as the net supply and demand (green). Panel (B) shows the validation and robustness checking across the bettor characteristics of expertise, bias, risk aversion, stubbornness and the variance of budgets. The left column shows the mean squared error introduced between the true outcome and the market price across a range of parameter values, and the right column shows the dominant lag. The dominant lag is the single lag $\ell$ whose one-variable regression of the outcome on the lagged market series yields the strongest statistical fit (lowest p-value). Each simulation has 100 agents over 100 time steps, with an initial price of 0.5 and the variance of the true election outcome 0.05. For each parameter value 30 simulations were performed and default values are $B_{i,0}\sim U(100,1000)$, $V_{i,0}\sim N(0.5,0.05)$, $C_{i,0}=0$, $s_i\sim \mathcal{N}(0.3,0.05)$, $e_i \sim \mathcal{N}(0.9,0.04)$, $r_i \sim U(0,1)$ as shown in \ref{['tbl:bettor_attributes']}. Red lines show the average value across the simulations with a 95% empirical confidence interval. Panel D shows the misclassification probability across different market price and true outcome pairs. As these values are further apart or closer to 0.5, the misclassification probability increases. The diagonal line marks perfect agreement between market and outcome. Regions near $\eta_t = 0.5$ and $m_t=0.5$ show a smooth transition between correct and incorrect classification. This transition becomes wider when uncertainty (noise) in either the market price or the true outcome increases, reflecting reduced confidence in whether the market’s implied prediction aligns with the eventual result.
• Figure 3: Panel A shows the mean squared error between market price and the proportion of budget allocated to a single whale bettor. The whale has a valuation of 0.6 (error of 0.1 above expected election outcome). As with Figure \ref{['fig:F1']} (B), each iteration has 100 agents across 100 timesteps. Here, 100 simulations are performed for each parameter value. All agents are initialized with an expertise of 0.95 to reduce the variance of market price. Default values for other attributes are given in \ref{['tbl:bettor_attributes']}. As the proportion of budget allocated to the whale increases, the error increases. Panel (B) shows the profit for non-whale bettors as a proportion of market capital. This plot shows that when a whale is present, the median return for agents with sufficiently high $e_i$ will increase. Panel (C) shows agreement between theoretical error introduced by a large whale ($\rho=0.5$) with varying bias and simulated results from the ABM.
• Figure 4: Panel A and B show results for how herding agents impact recovery after a market shock. The system is initialized with a single whale ($\rho=0.3$) and 100 agents with high expertise ($e_i=0.9$ and herding strengths $0,\;0.25,\;0.5,\; 0.75$ and $1$. Instability is visible for $h_i=1$ alongside a decreased rate of decay. Panel A shows the absolute market price error across time for each value of $h_i$ and Panel B shows snapshots at times 20, 50 and 100. For each value of $h_i$, 100 simulations were run. Panel C shows a visualization of phase diagram for some values of $\alpha$. A purple point labeled $h_i=1$ corresponds to the ABM setup with $h_i=1$ in panels A and B.
• Figure 5: Root mean squared error between Polymarket market price and Economist Forecast Model of state election returns in the 2016 and 2020 presidential elections.