Nonconvex Equilibrium Prices in Prediction Markets

Abstract

Prediction markets are increasingly being used to estimate probabilities of future events, and market equilibrium prices depend on the distribution of subjective probabilities of underlying events. When each contract requires the payment of a dollar if the underlying event were to occur, equilibrium prices are usually used to estimate the mean probabilities of the corresponding events. This paper shows that under certain conditions, market equilibrium prices of such contracts can lie outside the convex hull of potential traders’ probability beliefs, and where this occurs, market forecasts can induce stochastically dominated group decisions. We describe examples of where this could occur and generalize these examples to characterize conditions for nonconvex prices. A necessary condition for nonconvex prices is that market risk premia for complementary contracts have opposite signs. Preference functions on the lines of prospect theory have this property.