## Pricing combinatorial markets for tournaments (2008)

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### Other Repositories/Bibliography

Venue: | In Proc. of STOC |

Citations: | 20 - 15 self |

### BibTeX

@INPROCEEDINGS{Chen08pricingcombinatorial,

author = {Yiling Chen and Sharad Goel and David M. Pennock},

title = {Pricing combinatorial markets for tournaments},

booktitle = {In Proc. of STOC},

year = {2008},

pages = {305--314}

}

### OpenURL

### Abstract

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 2 n−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.

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Citation Context ...al it is NP-hard to compute, e.g., marginal probabilities P (Xi = xi). For certain network topologies, however, there exist efficient algorithms to compute both marginal and conditional distributions =-=[10; 15]-=-. In particular, for pricing tournaments, we rely on the fact that one can perform these computations on trees in time linear in the number of nodes. 3. Pricing Combinatorial Markets for Tournaments I... |

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Citation Context ...al it is NP-hard to compute, e.g., marginal probabilities P (Xi = xi). For certain network topologies, however, there exist efficient algorithms to compute both marginal and conditional distributions =-=[10; 15]-=-. In particular, for pricing tournaments, we rely on the fact that one can perform these computations on trees in time linear in the number of nodes. 3. Pricing Combinatorial Markets for Tournaments I... |

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