Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game
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.
|Date of creation:||2011|
|Date of revision:|
|Note:||View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00610840|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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.:
- Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2003.
"Shapley-like values for interval bankruptcy games,"
Other publications TiSEM
55aabb66-74af-4980-b6eb-f, Tilburg University, School of Economics and Management.
- 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.
- Aymeric Lardon, 2009. "The gamma-core in Cournot oligopoly TU-games with capacity constraints," Post-Print halshs-00544042, HAL.
- 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.
- Norde, H.W. & Pham Do, K.H. & Tijs, S.H., 2002.
"Oligopoly games with and without transferable technologies,"
Other publications TiSEM
0bc5059e-f4f3-42cd-a517-d, Tilburg University, School of Economics and Management.
- 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.
- Norde, H.W. & Pham Do, K.H. & Tijs, S.H., 2000. "Oligopoly Games With and Without Transferable Technologies," Discussion Paper 2000-66, Tilburg University, Center for Economic Research.
- 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.
- CHANDER, Parkash & TULKENS, Henry, 1995.
"The Core of an Economy with Multilateral Environmental Externalities,"
CORE Discussion Papers
1995050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Henry Tulkens & Parkash Chander, 1997. "The Core of an Economy with Multilateral Environmental Externalities," International Journal of Game Theory, Springer, vol. 26(3), pages 379-401.
- 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.
- Aymeric Lardon, 2010. "Cournot oligopoly interval games," Post-Print halshs-00544044, HAL.
- repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
- 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.
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 references are entirely missing, you can add them using this form.