Selling Data to an Agent with Endogenous Information

BSTRACTWe 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, 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. Moreover, assuming the valuation functions are linear, we fully characterize the revenue optimal mechanisms, which in general may be complex and contain a continuum of menu entries. However, we show that posting a deterministic price for revealing the states obtains at least half of the optimal revenue for arbitrary prior and cost functions. This leads to a sharp contrast to the exogenous information setting where the menu complexity can be unbounded for approximating the optimal revenue.