### Abstract

We focus on a permutation betting market under parimutuel call auction model where traders bet on final rankings of n candidates. We present a Proportional Betting mechanism for this market. Our mechanism allows traders to bet on any subset of the n ^{2} '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. Further, the formulation yields a set of n ^{2} unique marginal prices that are sufficient to price the bets in this mechanism, and are computable in polynomial-time. These marginal prices reflect the traders' beliefs about the marginal distributions over outcomes. More importantly, we 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 ^{2} 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, our algorithm addresses a generic problem of finding the maximum entropy distribution over permutations that has a given mean, and is of independent interest.

Original language | English (US) |
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Title of host publication | Internet and Network Economics - 4th International Workshop, WINE 2008, Proceedings |

Pages | 126-137 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 2008 |

Externally published | Yes |

Event | 4th International Workshop on Internet and Network Economics, WINE 2008 - Shanghai, China Duration: Dec 17 2008 → Dec 20 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5385 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th International Workshop on Internet and Network Economics, WINE 2008 |
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Country | China |

City | Shanghai |

Period | 12/17/08 → 12/20/08 |

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## Cite this

*Internet and Network Economics - 4th International Workshop, WINE 2008, Proceedings*(pp. 126-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5385 LNCS). https://doi.org/10.1007/978-3-540-92185-1_21