Price Interpretability of Prediction Markets: A Convergence Analysis.

This article investigates the convergence properties and price formation mechanisms in prediction markets using a novel multivariate utility (MU)-based market-making framework that unifies existing automated market-making schemes. It establishes that, under mild conditions, the wealth allocations of risk-averse traders with heterogeneous beliefs converge to a Pareto optimal distribution, and the market prices converge accordingly. For exponential utility–based markets, the limiting price equals the geometric mean of risk-adjusted trader beliefs; for convex risk measure–based markets, it corresponds to a weighted power mean of beliefs; and for markets with constant relative risk aversion (CRRA) utilities, the limiting price is characterized by a system of equations involving beliefs, risk parameters, and wealth, with trading sequence effects diminishing as the trader population grows. The authors propose an efficient approximation scheme based on Pareto optimality-induced (POI) weights to estimate limiting prices in finite markets, validated by numerical experiments demonstrating superior accuracy over existing methods. Additional analyses address price-volume relationships, forward-looking trader behavior, and market responses to nonstationary information, highlighting implications for market design and future research directions including empirical validation and incorporation of learning and behavioral models.