Trade-Based Asset Models for Combinatorial Prediction Markets

Abstract

A prediction market allows a group of traders to form a consensus probability distribution by entering into agreements that pay o ↵ con-tingent on events of interest. A combinatorial prediction market allows conditional trades or trades on Boolean combinations of events to form a joint distribution over many related events. Sun et al. (2012) showed how to use a junction tree to update both the consen-sus joint distribution and each user’s assets in a combinatorial prediction market. Be-cause a separate asset junction tree is main-tained for each user on the joint space, this approach is very inecient in the typical case where most users trade sparsely with respect to the joint space. Further, any changes to the global junction tree must be mirrored across all users. We demonstrate large ef-ficiency gains from divorcing the probability and asset data structures, dynamically build-ing a separate asset junction tree for each user. The trade-based asset model has as-set blocks as the basic units involving ques-tions being traded only. We compare a sim-ple block-iteration method against a more so-phisticated user-specific junction tree, ana-lyzing conditions under which each approach is faster. Our asset model has been deployed in SciCast1, a combinatorial prediction mar-ket for science and technology forecasting. 1