IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v76y2012i2p636-647.html
   My bibliography  Save this article

Optimal collusion under imperfect monitoring in multimarket contact

Author

Listed:
  • Kobayashi, Hajime
  • Ohta, Katsunori

Abstract

We investigate optimal collusion in repeated multimarket contact under imperfect public monitoring, where two firms operate in m markets and in each market, each firmʼs decision and public signals are binary. We show that in an optimal pure strategy strongly symmetric perfect public equilibrium, the size of efficiency loss is equal to that in the market with the most tempting deviation under single-market contact. Furthermore, we show a sufficient condition under which the symmetric equilibrium is optimal for joint payoff maximization among any perfect public equilibrium.

Suggested Citation

  • Kobayashi, Hajime & Ohta, Katsunori, 2012. "Optimal collusion under imperfect monitoring in multimarket contact," Games and Economic Behavior, Elsevier, vol. 76(2), pages 636-647.
    • Handle: RePEc:eee:gamebe:v:76:y:2012:i:2:p:636-647
    DOI: 10.1016/j.geb.2012.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825612001236
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2012.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December.
    2. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, March.
    3. Drew Fudenberg & David K. Levine & Satoru Takahashi, 2008. "Perfect public equilibrium when players are patient," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 16, pages 345-367, World Scientific Publishing Co. Pte. Ltd..
    4. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    5. Bentley W. MacLeod, 2003. "Optimal Contracting with Subjective Evaluation," American Economic Review, American Economic Association, vol. 93(1), pages 216-240, March.
    6. Drew Fudenberg & David K. Levine, 2008. "Efficiency and Observability with Long-Run and Short-Run Players," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 13, pages 275-307, World Scientific Publishing Co. Pte. Ltd..
    7. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    8. Matsushima, Hitoshi, 2001. "Multimarket Contact, Imperfect Monitoring, and Implicit Collusion," Journal of Economic Theory, Elsevier, vol. 98(1), pages 158-178, May.
    9. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    10. Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, vol. 78(3), pages 847-882, May.
    11. Hongbin Cai & Ichiro Obara, 2009. "Firm reputation and horizontal integration," RAND Journal of Economics, RAND Corporation, vol. 40(2), pages 340-363, June.
    12. Roy Radner & Roger Myerson & Eric Maskin, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 59-69.
    13. William N. Evans & Ioannis N. Kessides, 1994. "Living by the "Golden Rule": Multimarket Contact in the U. S. Airline Industry," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(2), pages 341-366.
    14. Spagnolo, Giancarlo, 1999. "On Interdependent Supergames: Multimarket Contact, Concavity, and Collusion," Journal of Economic Theory, Elsevier, vol. 89(1), pages 127-139, November.
    15. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    16. B. Douglas Bernheim & Michael D. Whinston, 1990. "Multimarket Contact and Collusive Behavior," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 1-26, Spring.
    17. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    18. Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(1), pages 233-265.
    19. Corwin D. Edwards, 1955. "Conglomerate Bigness as a Source of Power," NBER Chapters, in: Business Concentration and Price Policy, pages 331-359, National Bureau of Economic Research, Inc.
    20. Kobayashi, Hajime & Ohta, Katsunori, 2008. "Multimarket contact in continuous-time games," Economics Letters, Elsevier, vol. 101(1), pages 4-5, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Haizhen Lin & Ian M. McCarthy, 2023. "Multimarket Contact in Health Insurance: Evidence from Medicare Advantage," Journal of Industrial Economics, Wiley Blackwell, vol. 71(1), pages 212-255, March.
    2. Kobayashi, Hajime & Ohta, Katsunori & Sekiguchi, Tadashi, 2016. "Optimal sharing rules in repeated partnerships," Journal of Economic Theory, Elsevier, vol. 166(C), pages 311-323.
    3. Mitsuru Igami & Takuo Sugaya, 2022. "Measuring the Incentive to Collude: The Vitamin Cartels, 1990–99," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(3), pages 1460-1494.
    4. Tadashi Sekiguchi, 2013. "Multimarket Contact Under Demand Fluctuations: A Limit Result," Working Papers e052, Tokyo Center for Economic Research.
    5. Tadashi Sekiguchi, 2015. "Multimarket contact under demand fluctuations," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 1033-1048, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Osório António M., 2012. "A Folk Theorem for Games when Frequent Monitoring Decreases Noise," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-27, April.
    2. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
    3. Osório-Costa, António M., 2009. "Efficiency Gains in Repeated Games at Random Moments in Time," MPRA Paper 13105, University Library of Munich, Germany.
    4. Hongbin Cai & Ichiro Obara, 2009. "Firm reputation and horizontal integration," RAND Journal of Economics, RAND Corporation, vol. 40(2), pages 340-363, June.
    5. Hongbin Cai & Ichiro Obara, 2009. "Firm reputation and horizontal integration," RAND Journal of Economics, RAND Corporation, vol. 40(2), pages 340-363, June.
    6. Escobar, Juan F. & Llanes, Gastón, 2018. "Cooperation dynamics in repeated games of adverse selection," Journal of Economic Theory, Elsevier, vol. 176(C), pages 408-443.
    7. Hörner, Johannes & Takahashi, Satoru, 2016. "How fast do equilibrium payoff sets converge in repeated games?," Journal of Economic Theory, Elsevier, vol. 165(C), pages 332-359.
    8. Daehyun Kim & Ichiro Obara, 2023. "Asymptotic Value of Monitoring Structures in Stochastic Games," Papers 2308.09211, arXiv.org, revised Jul 2024.
    9. Hwa Ryung Lee, 2010. "Multimarket contact effect on collusion through diversification," IEW - Working Papers 501, Institute for Empirical Research in Economics - University of Zurich.
    10. Drew Fudenberg & David K. Levine, 2008. "Continuous time limits of repeated games with imperfect public monitoring," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 17, pages 369-388, World Scientific Publishing Co. Pte. Ltd..
    11. Kobayashi, Hajime & Ohta, Katsunori & Sekiguchi, Tadashi, 2016. "Optimal sharing rules in repeated partnerships," Journal of Economic Theory, Elsevier, vol. 166(C), pages 311-323.
    12. Osório Costa, Antonio Miguel, 2012. "The Limits of Discrete Time Repeated Games:Some Notes and Comments," Working Papers 2072/203171, Universitat Rovira i Virgili, Department of Economics.
    13. Laclau, Marie & Tomala, Tristan, 2017. "Repeated games with public deterministic monitoring," Journal of Economic Theory, Elsevier, vol. 169(C), pages 400-424.
    14. Fudenberg, Drew & Ishii, Yuhta & Kominers, Scott Duke, 2014. "Delayed-response strategies in repeated games with observation lags," Journal of Economic Theory, Elsevier, vol. 150(C), pages 487-514.
    15. Takizawa, Shinichiro, 2008. "The effect of decisions under uncertainty on imperfect monitoring games," Economics Letters, Elsevier, vol. 100(2), pages 165-168, August.
    16. Matsushima, Hitoshi, 2001. "Multimarket Contact, Imperfect Monitoring, and Implicit Collusion," Journal of Economic Theory, Elsevier, vol. 98(1), pages 158-178, May.
    17. Ichiro Obara, 2004. "Firm Reputation and Horizontal Integration (with H. Cai)," UCLA Economics Online Papers 318, UCLA Department of Economics.
    18. Kaplow, Louis & Shapiro, Carl, 2007. "Antitrust," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 2, chapter 15, pages 1073-1225, Elsevier.
    19. Pham, Tho & Talavera, Oleksandr & Yang, Junhong, 2016. "Multimarket Competition and Profitability: Evidence from Ukrainian banking," MPRA Paper 72376, University Library of Munich, Germany.
    20. Wilson, Alistair J. & Wu, Hong, 2017. "At-will relationships: How an option to walk away affects cooperation and efficiency," Games and Economic Behavior, Elsevier, vol. 102(C), pages 487-507.

    More about this item

    Keywords

    Multimarket contact; Infinitely repeated games; Imperfect public monitoring;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:76:y:2012:i:2:p:636-647. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.