Convexity and the Shapley value in Bertrand oligopoly TU-games with Shubik's demand functions
The 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.
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- 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.
- 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, 1994.
"The Core of an Economy With Multilateral Environmental Externalities,"
886, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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).
- 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, 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.
- repec:ner:tilbur:urn:nbn:nl:ui:12-89249 is not listed on IDEAS
- 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.
- Aymeric Lardon, 2010. "Convexity of Bertrand oligopoly TU-games with differentiated products," Post-Print halshs-00544056, HAL.
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