On Manipulation in Prediction Markets When Participants Influence Outcomes Directly

TL;DR

This paper models how prediction markets are affected when participants can influence the actual outcome, revealing two types of equilibria: truthful and collusive, which impact the reliability of market predictions.

Contribution

It introduces a novel two-stage game model capturing direct influence on outcomes and analyzes equilibrium behaviors in prediction markets.

Findings

LPP equilibria reveal expected outcomes based on private information.

HPP equilibria involve collusive, uninformative coordination.

The model demonstrates how influence can distort market predictions.

Abstract

Prediction markets are often used as mechanisms to aggregate information about a future event, for example, whether a candidate will win an election. The event is typically assumed to be exogenous. In reality, participants may influence the outcome, and therefore (1) running the prediction market could change the incentives of participants in the process that creates the outcome (for example, agents may want to change their vote in an election), and (2) simple results such as the myopic incentive compatibility of proper scoring rules no longer hold in the prediction market itself. We introduce a model of games of this kind, where agents first trade in a prediction market and then take an action that influences the market outcome. Our two-stage two-player model, despite its simplicity, captures two aspects of real-world prediction markets: (1) agents may directly influence the outcome, (2) some of the agents instrumental in deciding the outcome may not take part in the prediction market. We show that this game has two different types of perfect Bayesian equilibria, which we term LPP and HPP, depending on the values of the belief parameters: in the LPP domain, equilibrium prices reveal expected market outcomes conditional on the participants' private information, whereas HPP equilibria are collusive -- participants effectively coordinate in an uninformative and untruthful way.