TY - GEN

T1 - Price updating in combinatorial prediction markets with Bayesian networks

AU - Pennock, David M.

AU - Xia, Lirong

PY - 2011

Y1 - 2011

N2 - To overcome the #P-hardness of computing/ updating prices in logarithm market scoring rule-based (LMSR-based) combinatorial prediction markets, Chen et al. [5] recently used a simple Bayesian network to represent the prices of securities in combinatorial predictionmarkets for tournaments, and showed that two types of popular securities are structure preserving. In this paper, we significantly extend this idea by employing Bayesian networks in general combinatorial prediction markets. We reveal a very natural connection between LMSR-based combinatorial prediction markets and probabilistic belief aggregation, which leads to a complete characterization of all structure preserving securities for decomposable network structures. Notably, the main results by Chen et al. [5] are corollaries of our characterization. We then prove that in order for a very basic set of securities to be structure preserving, the graph of the Bayesian network must be decomposable. We also discuss some approximation techniques for securities that are not structure preserving.

AB - To overcome the #P-hardness of computing/ updating prices in logarithm market scoring rule-based (LMSR-based) combinatorial prediction markets, Chen et al. [5] recently used a simple Bayesian network to represent the prices of securities in combinatorial predictionmarkets for tournaments, and showed that two types of popular securities are structure preserving. In this paper, we significantly extend this idea by employing Bayesian networks in general combinatorial prediction markets. We reveal a very natural connection between LMSR-based combinatorial prediction markets and probabilistic belief aggregation, which leads to a complete characterization of all structure preserving securities for decomposable network structures. Notably, the main results by Chen et al. [5] are corollaries of our characterization. We then prove that in order for a very basic set of securities to be structure preserving, the graph of the Bayesian network must be decomposable. We also discuss some approximation techniques for securities that are not structure preserving.

UR - http://www.scopus.com/inward/record.url?scp=80053147052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053147052&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80053147052

T3 - Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011

SP - 581

EP - 588

BT - Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011

PB - AUAI Press

ER -