An Axiomatic Characterization of Continuous-Outcome Market Makers

Most existing market maker mechanisms for prediction markets are designed for events with a finite number of outcomes. All known attempts on designing market makers for forecasting continuous-outcome events resulted in mechanisms with undesirable properties. In this paper, we take an axiomatic approach to study whether it is possible for continuous-outcome market makers to satisfy certain desirable properties simultaneously. We define a general class of continuous-outcome market makers, which allows traders to express their information on any continuous subspace of their choice. We characterize desirable properties of these market makers using formal axioms. Our main result is an impossibility theorem showing that if a market maker offers binary-payoff contracts, either the market maker has unbounded worst case loss or the contract prices will stop being responsive, making future trades no longer profitable. In addition, we analyze a mechanism that does not belong to our framework. This mechanism has a worst case loss linear in the number of submitted orders, but encourages some undesirable strategic behavior.