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Selling supplemental information

Arlindo Skënderaj

Abstract

I consider an environment in which a decision maker faces uncertainty and privately holds information in the form of a signal about the true state of the world. The decision maker purchases additional information from a data broker before receiving the signal realization. I characterize the data broker's optimal selling mechanism, which involves screening over all possible signals. I allow the space of all signals the data broker can sell to be arbitrarily correlated with the signal the decision maker owns. This plays a key role in designing the optimal menu. In the binary action setting, the data broker extracts the efficient surplus by offering a distinct binary signal for each type. Moreover, this result holds even when the broker does not know the prior distribution over states. In more general environments, I provide conditions on the payoff structure and the decision maker's type space under which the data broker extracts the efficient surplus. I discuss scenarios in which efficient surplus extraction is not possible.

Selling supplemental information

Abstract

I consider an environment in which a decision maker faces uncertainty and privately holds information in the form of a signal about the true state of the world. The decision maker purchases additional information from a data broker before receiving the signal realization. I characterize the data broker's optimal selling mechanism, which involves screening over all possible signals. I allow the space of all signals the data broker can sell to be arbitrarily correlated with the signal the decision maker owns. This plays a key role in designing the optimal menu. In the binary action setting, the data broker extracts the efficient surplus by offering a distinct binary signal for each type. Moreover, this result holds even when the broker does not know the prior distribution over states. In more general environments, I provide conditions on the payoff structure and the decision maker's type space under which the data broker extracts the efficient surplus. I discuss scenarios in which efficient surplus extraction is not possible.

Paper Structure

This paper contains 27 sections, 7 theorems, 78 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Illustrative examples
  3. Example: Monopolist buying consumer data.
  4. Clinical diagnosis of a patient.
  5. Related Literature
  6. Model
  7. Information
  8. Value of supplemental information
  9. Data broker's problem
  10. Analysis
  11. Two types
  12. Binary actions
  13. Minimal complementary signal.
  14. Intuition behind Lemma \ref{['mainlemma']}
  15. Many states and many actions
  16. ...and 12 more sections

Key Result

Lemma 1

The optimal menu $(\sigma_L,t_L),(\sigma_H,t_H)$ is such that

Figures (4)

  • Figure 1: A signal.
  • Figure 2: The join of two signals.
  • Figure 3: Minimal complementary signal with two actions.
  • Figure 4: Intuition of Lemma \ref{['mainlemma']}.

Theorems & Definitions (16)

  • Definition 1
  • Lemma 1
  • Definition 2
  • Proposition 1
  • Lemma 2
  • Lemma 3
  • Proposition 2
  • Lemma 4
  • Proposition 3
  • proof
  • ...and 6 more