  We consider mechanisms for markets that are double-sided and have players
with multi-dimensional strategic spaces on at least one side. The players of
the market are strategic, and act to optimize their own utilities. The
mechanism designer, on the other hand, aims to optimize a social goal, i.e.,
the gain from trade. We focus on one example of this setting which is motivated
by the foreseeable future form of online advertising.
  Online advertising currently supports some of the most important Internet
services, including: search, social media and user generated content sites. To
overcome privacy concerns, it has been suggested to introduce user information
markets through information brokers into the online advertising ecosystem. Such
markets give users control over which data get shared in the online advertising
exchange. We describe a model for the above foreseeable future form of online
advertising, and design two mechanisms for the exchange of this model: a
deterministic mechanism which is related to the vast literature on mechanism
design through trade reduction and allows players with a multi-dimensional
strategic space, and a randomized mechanism which can handle a more general
version of the model.
