Combinatorial Information Market Design
Information Systems Frontiers
A dynamic pari-mutuel market for hedging, wagering, and information aggregation
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Algorithmic Game Theory
Pari-mutuel markets: mechanisms and performance
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
An optimization-based framework for automated market-making
Proceedings of the 12th ACM conference on Electronic commerce
Efficient Market Making via Convex Optimization, and a Connection to Online Learning
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
An axiomatic characterization of adaptive-liquidity market makers
Proceedings of the fourteenth ACM conference on Electronic commerce
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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.