Advanced Search
MyIDEAS: Login

Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game

Contents:

Author Info

  • Theo Driessen

    ()
    (Department of Applied Mathematics [Twente] - University of Twente)

  • Dongshuang Hou

    ()
    (Department of Applied Mathematics [Twente] - University of Twente)

  • Aymeric Lardon

    ()
    (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure de Lyon)

Abstract

In this article we consider Stackelberg oligopoly TU-games in gamma-characteristic function form (Chander and Tulkens 1997) in which any deviating coalition produces an output at a first period as a leader and outsiders simultaneously and independently play a quantity at a second period as followers. We assume that the inverse demand function is linear and that firms operate at constant but possibly distinct marginal costs. Generally speaking, for any TU-game we show that the 1-concavity property of its dual game is a necessary and sufficient condition under which the core of the initial game is non-empty and coincides with the set of imputations. The dual game of a Stackelberg oligopoly TU-game is of great interest since it describes the marginal contribution of followers to join the grand coalition by turning leaders. The aim is to provide a necessary and sufficient condition which ensures that the dual game of a Stackelberg oligopoly TU-game satisfies the 1-concavity property. Moreover, we prove that this condition depends on the heterogeneity of firms' marginal costs, i.e., the dual game is 1-concave if and only if firms' marginal costs are not too heterogeneous. This last result extends Marini and Currarini's core non-emptiness result (2003) for oligopoly situations.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://halshs.archives-ouvertes.fr/docs/00/61/08/40/PDF/Cooperative_Stackelberg_oligopoly_games.pdf
Download Restriction: no

Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00610840.

as in new window
Length:
Date of creation: 2011
Date of revision:
Handle: RePEc:hal:wpaper:halshs-00610840

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00610840/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/

Related research

Keywords: Stackelberg oligopoly TU-game; Dual game; 1-concavity;

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Chander, Parkash & Tulkens, Henry, 1994. "The Core of an Economy With Multilateral Environmental Externalities," Working Papers 886, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. Aymeric Lardon, 2010. "Cournot oligopoly interval games," Post-Print halshs-00544044, HAL.
  3. repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
  4. 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.
  5. Marini, Marco A. & Currarini, Sergio, 2003. "A sequential approach to the characteristic function and the core in games with externalities," MPRA Paper 1689, University Library of Munich, Germany, revised 2003.
  6. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2003. "Shapley-like values for interval bankruptcy games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121815, Tilburg University.
  7. Zhao, Jingang, 1999. "A necessary and sufficient condition for the convexity in oligopoly games," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 189-204, March.
  8. Aymeric Lardon, 2009. "The gamma-core in Cournot oligopoly TU-games with capacity constraints," Post-Print halshs-00544042, HAL.
  9. 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.
  10. 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.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-00610840. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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