Parimutuel Betting on Permutations

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dc.creatorAgrawal, Shipra
dc.creatorWang, Zizhuo
dc.creatorYe, Yinyu
dc.date2008-04-15
dc.date.accessioned2026-07-07T12:18:20Z
dc.date.available2026-07-07T12:18:20Z
dc.descriptionWe focus on a permutation betting market under parimutuel call auction model where traders bet on the final ranking of n candidates. We present a Proportional Betting mechanism for this market. Our mechanism allows the traders to bet on any subset of the n x n 'candidate-rank' pairs, and rewards them proportionally to the number of pairs that appear in the final outcome. We show that market organizer's decision problem for this mechanism can be formulated as a convex program of polynomial size. More importantly, the formulation yields a set of n x n unique marginal prices that are sufficient to price the bets in this mechanism, and are computable in polynomial-time. The marginal prices reflect the traders' beliefs about the marginal distributions over outcomes. We also propose techniques to compute the joint distribution over n! permutations from these marginal distributions. We show that using a maximum entropy criterion, we can obtain a concise parametric form (with only n x n parameters) for the joint distribution which is defined over an exponentially large state space. We then present an approximation algorithm for computing the parameters of this distribution. In fact, the algorithm addresses the generic problem of finding the maximum entropy distribution over permutations that has a given mean, and may be of independent interest.
dc.identifierhttps://arxiv.org/abs/0804.2288
dc.identifierhttp://arxiv.org/abs/0804.2288
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212373
dc.subjectComputer Science and Game Theory
dc.subjectComputational Complexity
dc.subjectData Structures and Algorithms
dc.subjectMultiagent Systems
dc.subjectI.2.1; F.2
dc.titleParimutuel Betting on Permutations
dc.typetext

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