Price Manipulation in Prediction Markets: Analysis and Mitigation

We consider the possible existence of a manipulator in a prediction market, whose incentive is to maximally increase the predicted probability of an event, and for whom profit or loss in the market is immaterial. We characterize the equilibria in a single-round market scoring rule (MSR), showing that the manipulator will play a strategy that mixes between pretending to have received one of the top signals. We propose a modification to the MSR in the form of trade limits, a maximum amount by which the price of the security can change at a given round. We show analytically that without a manipulator, this process converges to the true posterior, and computationally that in a market with a manipulator, the limits help reduce the distortion by the manipulator when traders do not know about the manipulator's existence. Specifically, we show through simulations that with high probability the honest traders will fully reveal their signals before the manipulator does, and that the price at this point of full revelation by the honest traders can be a significantly better approximation of the true posterior than the ultimate price reached, suggesting a rule by which the market should be stopped at that point.