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Screening with Advertisements

Kolagani Paramahamsa

TL;DR

This paper analyzes a two-dimensional screening problem where a seller monetizes a desirable good together with an advertising burden, receiving third-party revenue $k$ for ad exposure. Using the Daskalakis–Deckelbaum–Tzamos duality, the authors reformulate revenue as $\int u\,d\mu$ with a transformed measure $\mu$ that depends on $k$, and derive near-characterizations and tractability-friendly sufficiency tests for three practical pricing menus: Good-Only, Ad-Tiered, and Single-Bundle. A key contribution is the $k$-driven comparative static: low $k$ excludes the bad, intermediate $k$ supports a two-tier Ad-Tiered menu separating ad-tolerant and ad-averse buyers, and high $k$ bundles ads for all types, with a clean partition under uniform bad density. The framework yields interpretable geometric conditions (orthant tests) that simplify verifying optimality in two dimensions and informs pricing strategies for ad-supported digital services, while outlining natural extensions to richer, multi-dimensional settings.

Abstract

We investigate a seller's revenue-maximizing mechanism in a setting where a desirable good is sold together with an undesirable bad (e.g., advertisements) that generates third-party revenue. The buyer's private information is two-dimensional: valuation for the good and willingness to pay to avoid the bad. Following the duality framework of Daskalakis, Deckelbaum, and Tzamos (2017), whose results extend to our setting, we formulate the seller's problem using a transformed measure $μ$ that depends on the third-party payment $k$. We provide a near-characterization for optimality of three pricing mechanisms commonly used in practice -- the Good-Only, Ad-Tiered, and Single-Bundle Posted Price -- and introduce a new class of tractable, interpretable two-dimensional orthant conditions on $μ$ for sufficiency. Economically, $k$ yields a clean comparative static: low $k$ excludes the bad, intermediate $k$ separates ad-tolerant and ad-averse buyers, and high $k$ bundles ads for all types.

Screening with Advertisements

TL;DR

This paper analyzes a two-dimensional screening problem where a seller monetizes a desirable good together with an advertising burden, receiving third-party revenue for ad exposure. Using the Daskalakis–Deckelbaum–Tzamos duality, the authors reformulate revenue as with a transformed measure that depends on , and derive near-characterizations and tractability-friendly sufficiency tests for three practical pricing menus: Good-Only, Ad-Tiered, and Single-Bundle. A key contribution is the -driven comparative static: low excludes the bad, intermediate supports a two-tier Ad-Tiered menu separating ad-tolerant and ad-averse buyers, and high bundles ads for all types, with a clean partition under uniform bad density. The framework yields interpretable geometric conditions (orthant tests) that simplify verifying optimality in two dimensions and informs pricing strategies for ad-supported digital services, while outlining natural extensions to richer, multi-dimensional settings.

Abstract

We investigate a seller's revenue-maximizing mechanism in a setting where a desirable good is sold together with an undesirable bad (e.g., advertisements) that generates third-party revenue. The buyer's private information is two-dimensional: valuation for the good and willingness to pay to avoid the bad. Following the duality framework of Daskalakis, Deckelbaum, and Tzamos (2017), whose results extend to our setting, we formulate the seller's problem using a transformed measure that depends on the third-party payment . We provide a near-characterization for optimality of three pricing mechanisms commonly used in practice -- the Good-Only, Ad-Tiered, and Single-Bundle Posted Price -- and introduce a new class of tractable, interpretable two-dimensional orthant conditions on for sufficiency. Economically, yields a clean comparative static: low excludes the bad, intermediate separates ad-tolerant and ad-averse buyers, and high bundles ads for all types.
Paper Structure (29 sections, 78 equations, 3 figures)

This paper contains 29 sections, 78 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Related Literature
  3. A Screening Model with Ads
  4. Characterization Result of DDT
  5. Results
  6. Good-Only Posted Price
  7. The case without third--party payments
  8. Single-Bundle Posted Price
  9. Ad-Tiered Posted Price
  10. Uniform Distribution: Partitioning Third--Party Payment
  11. Economic Interpretation of the Three Regimes
  12. Uniform-bad density.
  13. Discussion
  14. MM Assumption: $k$-Shift
  15. Weakening Constant Third--Party Payment
  16. ...and 14 more sections

Figures (3)

  • Figure 1: Good-Only Posted Price
  • Figure 2: Single-Bundle Posted Price
  • Figure 3: Ad-Tiered Posted Price