  We consider a model of a data broker selling information to a single agent to
maximize his revenue. The agent has a private valuation of the additional
information, and upon receiving the signal from the data broker, the agent can
conduct her own experiment to refine her posterior belief on the states with
additional costs. To maximize expected revenue, only offering full information
in general is suboptimal, and the optimal mechanism may contain a continuum of
menu options with partial information to prevent the agent from having
incentives to acquire additional information from other sources. However, our
main result shows that the additional benefit from price discrimination is
limited, i.e., posting a deterministic price for revealing full information
obtains at least half of the optimal revenue for arbitrary prior and cost
functions.
