Convexity and the Shapley value in Bertrand oligopoly TU-games with Shubik's demand functions
AbstractThe Bertrand Oligopoly situation with Shubik's demand functions is modelled as a cooperative TU game. For that purpose two optimization problems are solved to arrive at the description of the worth of any coalition in the so-called Bertrand Oligopoly Game. Under certain circumstances, this Bertrand oligopoly game has clear affinities with the well-known notion in statistics called variance with respect to the distinct marginal costs. This Bertrand Oligopoly Game is shown to be totally balanced, but fails to be convex unless all the firms have the same marginal costs. Under the complementary circumstances, the Bertrand Oligopoly Game is shown to be convex and in addition, its Shapley value is fully determined on the basis of linearity applied to an appealing decomposition of the Bertrand Oligopoly Game into the difference between two convex games, besides two nonessential games. One of these two essential games concerns the square of one non- essential game.
Download InfoIf 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.
Bibliographic InfoPaper provided by HAL in its series Working Papers with number halshs-00610838.
Date of creation: 2011
Date of revision:
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00610838/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Bertrand Oligopoly situation; Bertrand Oligopoly Game; Convexity; Shapley Value; Total Balancedness.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-02 (All new papers)
- NEP-BEC-2011-08-02 (Business Economics)
- NEP-COM-2011-08-02 (Industrial Competition)
- NEP-GTH-2011-08-02 (Game Theory)
- NEP-HPE-2011-08-02 (History & Philosophy of Economics)
- NEP-IND-2011-08-02 (Industrial Organization)
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.:
- 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.
- Chander, P. & Tulkens, H., . "The core of an economy with multilateral environmental externalities," CORE Discussion Papers RP -1276, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Norde, H.W. & Pham Do, K.H. & Tijs, S.H., 2002.
"Oligopoly games with and without transferable technologies,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-89249, Tilburg University.
- 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.
- Aymeric Lardon, 2010. "Convexity of Bertrand oligopoly TU-games with differentiated products," Post-Print halshs-00544056, 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.
- 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.
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.