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.
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- 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.
- 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.
- repec:ner:tilbur:urn:nbn:nl:ui:12-89249 is not listed on IDEAS
- 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.
- 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, 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).
- 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).
- 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.
- 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.
- Aymeric Lardon, 2009. "The gamma-core in Cournot oligopoly TU-games with capacity constraints," Post-Print halshs-00544042, HAL.
- repec:ner:tilbur:urn:nbn:nl:ui:12-121815 is not listed on IDEAS
- Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003.
"Shapley-like values for interval bankruptcy games,"
AccessEcon, vol. 3(9), pages 1-8.
- Aymeric Lardon, 2010. "Cournot oligopoly interval games," Post-Print halshs-00544044, 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.
- repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
- 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.
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