Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Artificial intelligence: a modern approach
Artificial intelligence: a modern approach
Combinatorial Information Market Design
Information Systems Frontiers
Betting Boolean-style: a framework for trading in securities based on logical formulas
Decision Support Systems - Special issue: The fourth ACM conference on electronic commerce
Graphical Models for Groups: Belief Aggregation and Risk Sharing
Decision Analysis
Proceedings of the 8th ACM conference on Electronic commerce
Complexity of combinatorial market makers
Proceedings of the 9th ACM conference on Electronic commerce
Computational challenges in e-commerce
Communications of the ACM - Rural engineering development
Parimutuel Betting on Permutations
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Combinatorial prediction markets for event hierarchies
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Yoopick: a combinatorial sports prediction market
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
iSee: interactive scenario explorer for online tournament games
Proceedings of the International Conference on Advances in Computer Enterntainment Technology
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
A new understanding of prediction markets via no-regret learning
Proceedings of the 11th ACM conference on Electronic commerce
A practical liquidity-sensitive automated market maker
Proceedings of the 11th ACM conference on Electronic commerce
Price prediction in sports betting markets
MATES'10 Proceedings of the 8th German conference on Multiagent system technologies
An axiomatic characterization of continuous-outcome market makers
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Connections between markets and learning
ACM SIGecom Exchanges
An optimization-based framework for automated market-making
Proceedings of the 12th ACM conference on Electronic commerce
A tractable combinatorial market maker using constraint generation
Proceedings of the 13th ACM Conference on Electronic Commerce
An efficient Monte-Carlo algorithm for pricing combinatorial prediction markets for tournaments
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Using a case-based reasoning approach for trading in sports betting markets
Applied Intelligence
Efficient Market Making via Convex Optimization, and a Connection to Online Learning
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
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In a prediction market, agents trade assets whose value is tied to a future event, for example the outcome of the next presidential election. Asset prices determine a probability distribution over the set of possible outcomes. Typically, the outcome space is small, allowing agents to directly trade in each outcome, and allowing a market maker to explicitly update asset prices. Combinatorial markets, in contrast, work to estimate a full joint distribution of dependent observations, in which case the outcome space grows exponentially. In this paper, we consider the problem of pricing combinatorial markets for single-elimination tournaments. With $n$ competing teams, the outcome space is of size 2n-1. We show that the general pricing problem for tournaments is P-hard. We derive a polynomial-time algorithm for a restricted betting language based on a Bayesian network representation of the probability distribution. The language is fairly natural in the context of tournaments, allowing for example bets of the form "team i wins game k". We believe that our betting language is the first for combinatorial market makers that is both useful and tractable. We briefly discuss a heuristic approximation technique for the general case.