Recently, coinciding with and perhaps driving the increased popularity of prediction markets, several novel pari-mutuel mechanisms have been developed such as the logarithmic market-scoring rule (LMSR), the cost-function formulation of market makers, utility-based markets, and the sequential convex pari-mutuel mechanism (SCPM). In this work, we present a convex optimization framework that unifies these seemingly unrelated models for centrally organizing contingent claims markets. The existing mechanisms can be expressed in our unified framework by varying the choice of a concave value function. We show that this framework is equivalent to a convex risk minimization model for the market maker. This facilitates a better understanding of the risk attitudes adopted by various mechanisms. The unified framework also leads to easy implementation because we can now find the cost function of a market maker in polynomial time by solving a simple convex optimization problem. In addition to unifying and explaining the existing mechanisms, we use the generalized framework to derive necessary and sufficient conditions for many desirable properties of a prediction market mechanism such as proper scoring, truthful bidding (in a myopic sense), efficient computation, controllable risk measure, and guarantees on the worst-case loss. As a result, we develop the first proper, truthful, risk-controlled, loss-bounded (independent of the number of states) mechanism; none of the previously proposed mechanisms possessed all these properties simultaneously. Thus, our work provides an effective tool for designing new prediction market mechanisms. We also discuss possible applications of our framework to dynamic resource pricing and allocation in general trading markets.
- Decision analysis: risk
- Finance: asset pricing
- Games/group decisions: bidding/auctions, gambling
- Programming: convex, applications