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Consumer Privacy and the Incentives to Price-Discriminate in Online Markets

  • Alexandre de Cornière und Rodrigo Montes EMAIL logo
Veröffentlicht/Copyright: 19. September 2018
Review of Network Economics
Aus der Zeitschrift Review of Network Economics Band 16 Heft 3

Abstract

This paper studies how product customization and consumer privacy affect a monopolist’s incentives to engage in perfect price discrimination. We consider a monopolist that faces an ex ante choice to commit to price discrimination or to a uniform price. We introduce a simple model in which a monopolist can use analytics to access consumer data to both price-discriminate and offer customized products. In turn, consumers can protect their privacy to avoid price discrimination at a cost. By committing not to price-discriminate, the firm induces consumers to not protect their data, which allows it to customize the product. It can then extract the extra value through an increased uniform price. This strategy is profitable when the value added through customization is sufficiently high. An intermediate quality of analytics gives the monopolist more incentives to set a uniform price.

Keywords: analytics; big data; consumer privacy; customization; price discrimination

Acknowledgement

We thank Paul Belleflamme, Luc Bridet, Miaomiao Dong, Jay Ezrielev, Bruno Jullien, Regis Renault, Andrew Rhodes, Wilfried Sand-Zantman, and two anonymous referees for helpful comments. All remaining errors are our own.

Appendix

Proof of Proposition 1. Based on (1) we study the ten different cases that can arise. For a p^ that maximizes unconstrained profits in each case:

  1. If p<α≤1, then π(p)=(1−λ)p(1−p)+λp and p^1=12(1−λ).

  2. If p<1<α, then π(p)=(1−λ)p(1−p)+λp and p^1=12(1−λ).

  3. If α<p<1, then π(p)=(1−λ)p(1−p)+λp(1−p+α) and p^2=αλ+12.

  4. If p>α>1, then π(p)=λp(1−p+α) and p^3=1+α2.

  5. If p>1≥α, then π(p)=λp(1−p+α) and p^3=1+α2.

  6. If α>p>1, then π(p)=λp and p^4=+∞.

  7. If p=1≥α, then π(p)=λα.

  8. If p=1<α, then π(p)=λα.

  9. p=α>1, then π(p)=λα.

  10. p=α≤1, then π(p)=(1−λ)(1−α)α+λα.

In case 1, p^1 is a solution if 1≥α>12(1−λ) and λ < 12. In case 2, we require only λ < 12. In case 3, note that p^2 satisfies the constraint for α<12−λ<1. In cases 3 and 4, p^3 cannot satisfy the constraint for any values of α and λ. The same is true for case 6. In cases 7 to 10, we can see that choosing p = α weakly dominates choosing p = 1 by the monopolist. Finally, since the objective function may have two local maxima for some values of α and λ, we must compare the profits when p = α with π(p^1) when α>12(1−λ); and with π(p^2), when α<12−λ. First, we can show that

π(p^1)=14(1−λ)>(1−λ)(1−α)α+λα,

when 12>λ and 12(1−λ)<α≤1. Similarly, we verify that if λ<12 and α > 1,

π(p^1)>αλ⇔α<14λ(1−λ).

Second, we can show that, regardless of the value of λ,

π(p^2)=14(αλ+1)2>λα.

Proof of Proposition 2. The first order condition on (3) leads to p=1−λv^2(1−λ). Then plugging in v^=cλ+p leads to the equilibrium basic price and privacy share. Finally, remark that v^≤1⇔c≤λ2.

Proof of Proposition 3. First remark that if c>λ2 (i.e. no consumer pays for privacy) profits from PPD always exceed UP. For the rest of the proof we compare πPPD with the possible profit functions in Proposition 1:

  1. 14(αλ+1)2<πPPD if α2(λ−2)λ+2αλ+1>0, which holds when α<12−λ.

  2. (1−α)α(1−λ)+αλ<πPPD always holds.

  3. 14(1−λ)<πPPD if 4α(λ−1)+1<0⇔α<14(1−λ).

  4. Solve for α in αλ≥πPPD. Then verify α^ satisfies the constrains in Proposition 1.

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Published Online: 2018-09-19
Published in Print: 2017-09-26

©2017 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. Special Issue on “Economics of Digitization”
  4. Articles
  5. Following the Code: Spillovers and Knowledge Transfer
  6. The Value of Consumer Data in Online Advertising
  7. Consumer Privacy and the Incentives to Price-Discriminate in Online Markets
  8. Who Pays for Card Payments? A General Model on the Role of Interchange Fees
https://doi.org/10.1515/rne-2018-0004
Schlagwörter für diesen Artikel
analytics; big data; consumer privacy; customization; price discrimination

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. Special Issue on “Economics of Digitization”
  4. Articles
  5. Following the Code: Spillovers and Knowledge Transfer
  6. The Value of Consumer Data in Online Advertising
  7. Consumer Privacy and the Incentives to Price-Discriminate in Online Markets
  8. Who Pays for Card Payments? A General Model on the Role of Interchange Fees
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