Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Bidding and allocation in combinatorial auctions
Proceedings of the 2nd ACM conference on Electronic commerce
Computationally feasible VCG mechanisms
Proceedings of the 2nd ACM conference on Electronic commerce
Forecasting uncertain events with small groups
Proceedings of the 3rd ACM conference on Electronic Commerce
Extracting collective probabilistic forecasts from web games
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Winner determination in combinatorial auction generalizations
Proceedings of the first international joint conference on Autonomous agents and multiagent systems: part 1
Combinatorial Information Market Design
Information Systems Frontiers
Compact Securities Markets for Pareto Optimal Reallocation of Risk
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Information incorporation in online in-Game sports betting markets
Proceedings of the 4th ACM conference on Electronic commerce
Combinatorial Auctions: A Survey
INFORMS Journal on Computing
A dynamic pari-mutuel market for hedging, wagering, and information aggregation
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Parimutuel Betting on Permutations
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Pari-mutuel markets: mechanisms and performance
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Automated market-making in the large: the gates hillman prediction market
Proceedings of the 11th ACM conference on Electronic commerce
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We develop a framework for trading in compound securities: financial instruments that pay off contingent on the outcomes of arbitrary statements in propositional logic. Buying or selling securities---which can be thought of as betting on or against a particular future outcome---allows agents both to hedge risk and to profit (in expectation) on subjective predictions. A compound securities market allows agents to place bets on arbitrary boolean combinations of events, enabling them to more closely achieve their optimal risk exposure, and enabling the market as a whole to more closely achieve the social optimum.The tradeoff for allowing such expressivity is in the complexity of the agents' and auctioneer's optimization problems.We develop and motivate the concept of a compound securities market, presenting the framework through a series of formal definitions and examples. We then analyze in detail the auctioneer's matching problem. We show that, with numevents events, the matching problem is co-NP-complete in the divisible case and complete in the indivisible case. We show that the latter hardness result holds even under severe language restrictions on bids. With events, and numevents securities, the problem is polynomial in the divisible case and NP-complete in the indivisible case. We briefly discuss matching algorithms and tractable special cases.