  We consider the model of the data broker selling information to a single
agent to maximize his revenue. The agent has private valuation for 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. In this paper, we show that in the optimal
mechanism, there is no distortion at the top and the agent has no incentive to
acquire any additional costly information under equilibrium. Still, the ability
to acquire additional information distorts the incentives of the agent, and
reduces the optimal revenue of the data broker. Finally, we show that posting a
deterministic price on fully revealing the states is optimal when the prior
distribution is sufficiently informative.
