Combinatorial prediction markets for event hierarchies
نویسندگان
چکیده
We study combinatorial prediction markets where agents bet on the sum of values at any tree node in a hierarchy of events, for example the sum of page views among all the children within a web subdomain. We propose three expressive betting languages that seem natural, and analyze the complexity of pricing using Hanson’s logarithmic market scoring rule (LMSR) market maker. Sum of arbitrary subset (SAS) allows agents to bet on the weighted sum of an arbitrary subset of values. Sum with varying weights (SVW) allows agents to set their own weights in their bets but restricts them to only bet on subsets that correspond to tree nodes in a fixed hierarchy. We show that LMSR pricing is NP-hard for both SAS and SVW. Sum with predefined weights (SPW) also restricts bets to nodes in a hierarchy, but using predefined weights. We derive a polynomial time pricing algorithm for SPW. We discuss the algorithm’s generalization to other betting contexts, including betting on maximum/minimum and betting on the product of binary values. Finally, we describe a prototype we built to predict web site page views and discuss the implementation issues that arose.
منابع مشابه
Probability and Asset Updating using Bayesian Networks for Combinatorial Prediction Markets
A market-maker-based prediction market lets forecasters aggregate information by editing a consensus probability distribution either directly or by trading securities that pay off contingent on an event of interest. Combinatorial prediction markets allow trading on any event that can be specified as a combination of a base set of events. However, explicitly representing the full joint distribut...
متن کاملCombinatorial Prediction Markets
Several hundred organizations are now using prediction markets to forecast sales, project completion dates, and more. This number has been doubling annually for several years. Most, however, are simple prediction markets, with one market per number forecast, and several traders per market. In contrast, a single combinatorial prediction market lets a few traders manage an entire combinatorial sp...
متن کاملPrice Updating in Combinatorial Prediction Markets with Bayesian Networks
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 prediction markets for tournaments, and showed that two types of popular securities are structure preserving. In this paper, we significantly e...
متن کاملCombinatorial Modelling and Learning with Prediction Markets
Combining models in appropriate ways to achieve high performance is commonly seen in machine learning fields today. Although a large amount of combinatorial models have been created, little attention is drawn to the commons in different models and their connections. A general modelling technique is thus worth studying to understand model combination deeply and shed light on creating new models....
متن کاملElectronic Markets and Electronic Hierarchies: effects of Information Technology on Market Structur Corporate Strategies
This paper analyzes the fundamental changes in market structures that may result from the increasing use of information teChnology. First, an analytic framework is presented and its usefulness is demonstrated in explaining several major historical changes in American business structures. Then, the framework is used to help explain how electronic markets and electronic hierarchies will allow clo...
متن کامل