Bidding and allocation in combinatorial auctions
Proceedings of the 2nd ACM conference on Electronic commerce
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Introduction to Algorithms
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
Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combinatorial Auctions
ACM SIGecom Exchanges
Pricing combinatorial markets for tournaments
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Self-financed wagering mechanisms for forecasting
Proceedings of the 9th ACM conference on Electronic commerce
Permutation betting markets: singleton betting with extra information
Proceedings of the 9th ACM conference on Electronic commerce
Complexity of combinatorial market makers
Proceedings of the 9th ACM conference on Electronic commerce
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
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Prediction markets, mechanism design, and cooperative game theory
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
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
Efficient Market Making via Convex Optimization, and a Connection to Online Learning
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
What you jointly know determines how you act: strategic interactions in prediction markets
Proceedings of the fourteenth ACM conference on Electronic commerce
Cost function market makers for measurable spaces
Proceedings of the fourteenth ACM conference on Electronic commerce
| Hi-index | 0.00 |
We consider a permutation betting scenario, where people wager on the final ordering of n candidates: for example, the outcome of a horse race. We examine the auctioneer problem of risklessly matching up wagers or, equivalently, finding arbitrage opportunities among the proposed wagers. Requiring bidders to explicitly list the orderings that they'd like to bet on is both unnatural and intractable, because the number of orderings is n! and the number of subsets of orderings is 2n!. We propose two expressive betting languages that seem natural for bidders, and examine the computational complexity of the auctioneer problem in each case. Subset betting allows traders to bet either that a candidate will end up ranked among some subset of positions in the final ordering, for example, "horse A will finish in positions 4, 9, or 13-21", or that a position will be taken by some subset of candidates, for example "horse A, B, or D will finish in position 2". For subset betting, we show that the auctioneer problem can be solved in polynomial time if orders are divisible. Pair betting allows traders to bet on whether one candidate will end up ranked higher than another candidate, for example "horse A will beat horse B". We prove that the auctioneer problem becomes NP-hard for pair betting. We identify a sufficient condition for the existence of a pair betting match that can be verified in polynomial time. We also show that a natural greedy algorithm gives a poor approximation for indivisible orders.