How Bad is the Merger Paradox?

Liad Blumrosen, Yehonatan Mizrahi*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The merger paradox is a classic, counter-intuitive result from the literature of Industrial Organization saying that merging firms typically experience a decline in their overall profit compared to their total pre-merger profit. This phenomenon is more striking in small oligopolistic markets, where mergers increase market concentration and may hence trigger a substantial increase in prices. In this paper, we investigate the severity of the merger paradox in Cournot oligopoly markets. Namely, we study the worst-case magnitude of this profit loss in quantity-setting market games. We consider convex, asymmetric production costs for the firms, and we show that the profit loss can be substantial even in small markets. That is, two merging firms can lose half of their pre-merger profit, but no more than half in markets with concave demand functions. On the positive side, we show that in markets with affine demand two firms can never lose more than 1/9 of their profit when merging, and this bound is tight. We also study the asymptotic loss in larger markets, where it is easy to show that the profit loss can be arbitrarily large when multiple firms merge; we give bounds that characterize the profit loss from a merger as a function of the market size and the number of merging firms.

Original languageAmerican English
Title of host publicationAlgorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
EditorsPanagiotis Kanellopoulos, Maria Kyropoulou, Alexandros Voudouris
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages18
ISBN (Print)9783031157134
StatePublished - 2022
Event15th International Symposium on Algorithmic Game Theory, SAGT 2022 - Colchester, United Kingdom
Duration: 12 Sep 202215 Sep 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13584 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Symposium on Algorithmic Game Theory, SAGT 2022
Country/TerritoryUnited Kingdom

Bibliographical note

Funding Information:
Acknowledgements. This research was supported by the Israel Science Foundation grant number 2570/19 and by the Asper center in the Hebrew University Business School.

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.


  • Approximation
  • Cournot Oligopoly
  • Industrial Organization
  • Market Structure
  • Mergers and Acquisitions
  • Nash Equilibrium


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