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Data and Competitive Markets: Some Notes on Competition, Concentration and Welfare

  • António Osório ORCID logo EMAIL logo
Published/Copyright: June 2, 2022
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 23 Issue 1

Abstract

Companies are increasingly using data to predict behavior and improve the relation with their customers. In this context, data exchange raises important concerns regarding competition, concentration and welfare. This paper presents a novel linear demand approach that captures data and information effects in competitive markets, which are conveniently summarized in a precision parameter. Subsequently, the proposed approach is applied to study the firm’s incentives to exchange data and their impact in fundamental market variables, welfare and market concentration measures. We found that the incentives for data exchange between competitor firms emerge when the individual information gains are strong enough to compensate for the competitor’s information gains, and the associated strategic correlation effect between varieties. The results also suggest that market concentration tends to increase after data exchange, but both consumers and producers benefit from it. The reason is that better data allows firms to positioning closer to consumers’ needs.

Keywords: data; data exchange; linear demand; consumer targeting; competitive markets
JEL Classification: D11; L11; L40
Corresponding author: António Osório, Dept. Economics, Universitat Rovira i Virgili and ECO-SOS, Tarragona, Spain, E-mail:

Acknowledgments

Support from the GRODE, Universitat Rovira i Virgili and the Spanish Ministry of Science and Innovation Project RTI2018-094733-B-100 (AEI/FEDER, UE) and PID2019-105982GB-100 is gratefully acknowledged. I would like to thank Juan Pablo Rincón-Zapatero, as well as several seminars and congress participants for helpful comments and discussions. The usual caveat applies.

Appendix: Proofs of the Results

Proof of Corollary 1

The proof is obtained by verifying the sign of the derivative of q j , p j , π j , q k , p k and π k with respect to ρ j and k ≠ j, under the assumption that a − c ≥ α n / ρ j − ∑ k ≠ j n 1 / ρ k for all j. □

Proof of Corollary 2

The proof is obtained by verifying the sign of the derivative of q 1, p 1, π 1, q 2, p 2 and π 2 with respect to ρ 1 (or ρ 1), under the assumption that 2 ρ 1 ≥ s ρ 2 and 2 ρ 2 ≥ s ρ 1 . □

Proof of Proposition 3 and Corollary 3

In the additive n-firms model, the profit of firm j in Expression (6) after having exchanged data with firm k becomes:

π j ′ = a − c − ( n − 1 ) α / ρ j + k + α ∑ l ≠ k , j n 1 / ρ l 2 / ( ( n + 1 ) b ) 2 ,

for j = 1, …, n. After some algebra, for ρ j ≥ ρ k , this profit is higher than the profit before exchanging data, which is given by Expression (6). In other words, π j ′ ≥ π j if inequality (14) is satisfied. Otherwise, if ρ j ≤ ρ k , inequality (14) is always satisfied. In the symmetric case, i.e. ρ j = ρ k , inequality (14) is always satisfied because n ≥ 1 and ρ j+k ≥ ρ j . □

Proof of Proposition 4

Simply compare q j ′ ≥ q j and p j ′ ≥ p j to obtain again inequality (14). □

Proof of Proposition 5 and Corollary 4

In the multiplicative 2-firms model, the profit of firm j in Expression (13) after exchanging data with firm k becomes:

π j ′ = ( a − c ) 2 ρ j + k ( 2 − s ′ ) 2 / ( b ( 4 − s ′ 2 ) 2 ) ,

for j = 1, 2, where s ′ = s j k ′ = s k j ′ ≥ s is the degree of substitution after the data exchange. After some algebra, this profit is higher than the profit before exchanging data, which is given by Expression (13), i.e. π j ′ ≥ π j , if inequality (15) is satisfied. In the symmetric case, i.e. ρ j = ρ k , inequality (15) becomes ρ j+k /(2 + s′)2 ≥ ρ j /(2 + s)2, which is satisfied if ρ j+k is sufficiently larger than ρ j and/or s′ is not too larger than s. □

Proof of Proposition 6

In the multiplicative 2-firms model, the equilibrium quantity and price of firm j in Expressions (11) and (12), respectively, after having exchanged data with firm k become:

q j ′ = ( a − c ) ρ j + k / b ( 2 + s ′ ) ,

and,

p j ′ = a ( 2 − s ′ ) + c ( 2 + s ′ − s ′ 2 ) / ( 4 − s ′ 2 ) ,

respectively.

The firm j quantity after the data exchange is larger than before, which is given by Expression (11), i.e. q j ′ ≥ q j , if the following inequality is satisfied:

(16) ρ j + k ≥ ( 2 + s ′ ) ρ j ( 2 ρ j − s ρ k ) ( 2 + s ) ( 2 − s ) .

If inequality (16) is true for ρ j ≥ ρ k , then it is also true for ρ j ≤ ρ k because the right-hand side becomes smaller. Then, for ρ j ≥ ρ k , inequality (16) is satisfied if inequality (15) is also satisfied, i.e. if the right-hand side of inequality (15) is larger than the right-hand side of inequality (16), i.e. if:

( 2 + s ′ ) 2 ( 2 ρ j − s ρ k ) 2 ( 2 + s ) 2 ( 2 − s ) 2 ≥ ( 2 + s ′ ) ρ j ( 2 ρ j − s ρ k ) ( 2 + s ) ( 2 − s ) .

After some algebra, this inequality becomes ( 2 + s ′ ) ( 2 − s ρ k / ρ j ) ≥ ( 2 + s ) ( 2 − s ) , which is more difficult to satisfy if s′ = s, and in this case becomes ( 2 − s ρ k / ρ j ) / ( 2 − s ) ≥ 1 . Then, if ρ k /ρ j ≤ 1 this inequality is always satisfied because the numerator is larger than the denominator. Consequently, if inequality (16) is satisfied for ρ k /ρ j ≤ 1, it is also satisfied for ρ k /ρ j ≥ 1. Symmetry is just a particular case. Therefore, if there exist incentives for data exchange, then both firms’ equilibrium quantities increase.

Now consider the prices. The firm j price after the data exchange is lower than before, which is given by Expression (12), i.e. p j ′ ≤ p j , if the following inequality is satisfied:

2 ( a + c ) − ( a − c ) s ′ − c s ′ 2 ( 4 − s ′ 2 ) ≤ 2 ( a + c ) − ( a − c ) s ρ k / ρ j − c s 2 ( 4 − s 2 ) .

After some algebra this inequality reduces to ρ k / ρ j ≤ ( 2 s ′ + s 2 ) / ( s ( 2 + s ′ ) ) . The right-hand side increases in s′ and decreases in s, therefore, it takes the minimum value ρ k / ρ j ≤ 1 at s = s′. Therefore, if ρ k /ρ j ≤ 1, firm j always decreases prices after the data exchange, which includes the symmetric case, but not necessarily the case ρ k /ρ j > 1. □

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Received: 2021-07-01
Revised: 2022-03-28
Accepted: 2022-05-23
Published Online: 2022-06-02

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Duty to Read vs Duty to Disclose Fine Print. Does the Market Structure Matter?
  4. Cobb-Douglas Preferences and Pollution in a Bilateral Oligopoly Market
  5. Epsilon-Efficiency in a Dynamic Partnership with Adverse Selection and Moral Hazard
  6. Management Turnover, Strategic Ambiguity and Supply Incentives
  7. Uninformed Bidding in Sequential Auctions
  8. Arrowian Social Equilibrium: Indecisiveness, Influence and Rational Social Choices under Majority Rule
  9. Family Ties and Corruption
  10. Social Efficiency of Entry in a Vertical Structure with Third Degree Price Discrimination
  11. Insufficient Entry and Consumer Search
  12. Quality Competition and Market-Share Leadership in Network Industries
  13. The Effects of Introducing Advertising in Pay TV: A Model of Asymmetric Competition between Pay TV and Free TV
  14. Redistributive Unemployment Benefit and Taxation
  15. Constrained Persuasion with Private Information
  16. A Dynamic Graph Model of Strategy Learning for Predicting Human Behavior in Repeated Games
  17. Relative Income Concerns, Dismissal, and the Use of Pay-for-Performance
  18. Delegation in Vertical Relationships: The Role of Reciprocity
  19. Step by Step Innovation without Mutually Exclusive Patenting: Implications for the Inverted U
  20. Data and Competitive Markets: Some Notes on Competition, Concentration and Welfare
  21. Notes
  22. Optimality of a Linear Decision Rule in Discrete Time AK Model
  23. Equilibrium Pricing under Concave Advertising Costs
https://doi.org/10.1515/bejte-2021-0087
Keywords for this article
data; data exchange; linear demand; consumer targeting; competitive markets

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Duty to Read vs Duty to Disclose Fine Print. Does the Market Structure Matter?
  4. Cobb-Douglas Preferences and Pollution in a Bilateral Oligopoly Market
  5. Epsilon-Efficiency in a Dynamic Partnership with Adverse Selection and Moral Hazard
  6. Management Turnover, Strategic Ambiguity and Supply Incentives
  7. Uninformed Bidding in Sequential Auctions
  8. Arrowian Social Equilibrium: Indecisiveness, Influence and Rational Social Choices under Majority Rule
  9. Family Ties and Corruption
  10. Social Efficiency of Entry in a Vertical Structure with Third Degree Price Discrimination
  11. Insufficient Entry and Consumer Search
  12. Quality Competition and Market-Share Leadership in Network Industries
  13. The Effects of Introducing Advertising in Pay TV: A Model of Asymmetric Competition between Pay TV and Free TV
  14. Redistributive Unemployment Benefit and Taxation
  15. Constrained Persuasion with Private Information
  16. A Dynamic Graph Model of Strategy Learning for Predicting Human Behavior in Repeated Games
  17. Relative Income Concerns, Dismissal, and the Use of Pay-for-Performance
  18. Delegation in Vertical Relationships: The Role of Reciprocity
  19. Step by Step Innovation without Mutually Exclusive Patenting: Implications for the Inverted U
  20. Data and Competitive Markets: Some Notes on Competition, Concentration and Welfare
  21. Notes
  22. Optimality of a Linear Decision Rule in Discrete Time AK Model
  23. Equilibrium Pricing under Concave Advertising Costs
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