IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v47y2018i1d10.1007_s00182-017-0584-8.html
   My bibliography  Save this article

Optimal deterrence of cooperation

Author

Listed:
  • Stéphane Gonzalez

    (Univ Lyon, UJM Saint-Etienne, CNRS, GATE L-SE UMR 5824)

  • Aymeric Lardon

    (Université Côte d’Azur, GREDEG, CNRS)

Abstract

We introduce axiomatically a new solution concept for cooperative games with transferable utility inspired by the core. While core solution concepts have investigated the sustainability of cooperation among players, our solution concept, called contraction core, focuses on the deterrence of cooperation. The main interest of the contraction core is to provide a monetary measure of the robustness of cooperation in the grand coalition. We motivate this concept by providing optimal fine imposed by competition authorities for the dismantling of cartels in oligopolistic markets. We characterize the contraction core on the set of balanced cooperative games with transferable utility by four axioms: the two classic axioms of non-emptiness and individual rationality, a superadditivity principle and a weak version of a new axiom of consistency.

Suggested Citation

  • Stéphane Gonzalez & Aymeric Lardon, 2018. "Optimal deterrence of cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 207-227, March.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:1:d:10.1007_s00182-017-0584-8
    DOI: 10.1007/s00182-017-0584-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-017-0584-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-017-0584-8?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. d'Aspremont, Claude & Jacquemin, Alexis, 1988. "Cooperative and Noncooperative R&D in Duopoly with Spillovers," American Economic Review, American Economic Association, vol. 78(5), pages 1133-1137, December.
    2. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    3. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    4. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    5. Driessen, Theo S.H. & Meinhardt, Holger I., 2005. "Convexity of oligopoly games without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 102-126, July.
    6. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    7. Stéphane Gonzalez & Michel Grabisch, 2015. "Preserving coalitional rationality for non-balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 733-760, August.
    8. Zhao, J, 1996. "A B-Core Existence Result and its Application to Oligopoly Markets," ISER Discussion Paper 0418, Institute of Social and Economic Research, Osaka University.
    9. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    10. Calleja, Pedro & Rafels, Carles & Tijs, Stef, 2009. "The aggregate-monotonic core," Games and Economic Behavior, Elsevier, vol. 66(2), pages 742-748, July.
    11. Walter Trockel, 2005. "Core-equivalence for the Nash bargaining solution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(1), pages 255-263, January.
    12. Norde, Henk & Pham Do, Kim Hang & Tijs, Stef, 2002. "Oligopoly games with and without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 187-207, March.
    13. Paraskevas Lekeas & Giorgos Stamatopoulos, 2014. "Cooperative oligopoly games with boundedly rational firms," Annals of Operations Research, Springer, vol. 223(1), pages 255-272, December.
    14. Aymeric Lardon, 2012. "The γ-core in Cournot oligopoly TU-games with capacity constraints," Theory and Decision, Springer, vol. 72(3), pages 387-411, March.
    15. Jingang Zhao, 2001. "The relative interior of the base polyhedron and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 635-648.
    16. Zhao, Jingang, 1999. "A [beta]-Core Existence Result and Its Application to Oligopoly Markets," Games and Economic Behavior, Elsevier, vol. 27(1), pages 153-168, April.
    17. John G. Cross, 1967. "Some theoretic characteristics of economic and political coalitions," Journal of Conflict Resolution, Peace Science Society (International), vol. 11(2), pages 184-195, June.
    18. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    19. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    20. Camelia Bejan & Juan Gómez, 2009. "Core extensions for non-balanced TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 3-16, March.
    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. Aymeric Lardon, 2017. "On the Coalitional Stability of Monopoly Power in Differentiated Bertrand and Cournot Oligopolies," GREDEG Working Papers 2017-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    2. João Ricardo Faria & Peter F. Wanke & João J. Ferreira & Franklin G. Mixon, 2018. "Research and innovation in higher education: empirical evidence from research and patenting in Brazil," Scientometrics, Springer;Akadémiai Kiadó, vol. 116(1), pages 487-504, July.
    3. Aymeric Lardon, 2019. "On the coalitional stability of monopoly power in differentiated Bertrand and Cournot oligopolies," Theory and Decision, Springer, vol. 87(4), pages 421-449, 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. Aymeric Lardon, 2019. "On the coalitional stability of monopoly power in differentiated Bertrand and Cournot oligopolies," Theory and Decision, Springer, vol. 87(4), pages 421-449, November.
    2. Aymeric Lardon, 2017. "On the Coalitional Stability of Monopoly Power in Differentiated Bertrand and Cournot Oligopolies," GREDEG Working Papers 2017-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    3. Aymeric Lardon, 2017. "Endogenous interval games in oligopolies and the cores," Annals of Operations Research, Springer, vol. 248(1), pages 345-363, January.
    4. Stamatopoulos, Giorgos, 2018. "Cooperative games with externalities and probabilistic coalitional beliefs," MPRA Paper 92862, University Library of Munich, Germany.
    5. Aymeric Lardon, 2020. "Convexity of Bertrand oligopoly TU-games with differentiated products," Annals of Operations Research, Springer, vol. 287(1), pages 285-302, April.
    6. Dongshuang Hou & Aymeric Lardon & T. S. H. Driessen, 2017. "Stackelberg Oligopoly TU-Games: Characterization and Nonemptiness of the Core," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-16, December.
    7. Paraskevas Lekeas & Giorgos Stamatopoulos, 2016. "Cooperative Games with Externalities and Probabilistic Coalitional Beliefs," Working Papers 1605, University of Crete, Department of Economics.
    8. Takeda, Kohei & Hosoe, Toyoki & Watanabe, Takayuki & Matsubayashi, Nobuo, 2018. "Stability analysis of horizontal mergers in a market with asymmetric substitutability," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 73-84.
    9. Zhao, Jingang, 2018. "Three little-known and yet still significant contributions of Lloyd Shapley," Games and Economic Behavior, Elsevier, vol. 108(C), pages 592-599.
    10. Aymeric Lardon, 2014. "A Partial Characterization of the Core in Bertrand Oligopoly TU-games with Transferable Technologies," GREDEG Working Papers 2014-33, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    11. Theo Driessen & Dongshuang Hou & Aymeric Lardon, 2011. "Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game," Working Papers halshs-00610840, HAL.
    12. Dongshuang Hou & Theo Driessen & Aymeric Lardon, 2011. "Convexity and the Shapley value in Bertrand oligopoly TU-games with Shubik's demand functions," Working Papers halshs-00610838, HAL.
    13. Meinhardt, Holger Ingmar, 2020. "On the Replication of the Pre-Kernel and Related Solutions," MPRA Paper 102676, University Library of Munich, Germany.
    14. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    15. Sergio Currarini & Marco A. Marini, 2015. "Coalitional Approaches to Collusive Agreements in Oligopoly Games," Manchester School, University of Manchester, vol. 83(3), pages 253-287, June.
    16. Jean Derks & Hans Peters & Peter Sudhölter, 2014. "On extensions of the core and the anticore of transferable utility games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 37-63, February.
    17. Paraskevas Lekeas & Giorgos Stamatopoulos, 2014. "Cooperative oligopoly games with boundedly rational firms," Annals of Operations Research, Springer, vol. 223(1), pages 255-272, December.
    18. Aymeric Lardon, 2012. "The γ-core in Cournot oligopoly TU-games with capacity constraints," Theory and Decision, Springer, vol. 72(3), pages 387-411, March.
    19. Fatma Aslan & Papatya Duman & Walter Trockel, 2019. "Duality for General TU-games Redefined," Working Papers CIE 121, Paderborn University, CIE Center for International Economics.
    20. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.

    More about this item

    Keywords

    TU-game; Contraction core; Optimal fine; Cournot oligopoly; Axiomatization;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

    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:spr:jogath:v:47:y:2018:i:1:d:10.1007_s00182-017-0584-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.