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The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier / Wenzelburger, Jan


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1935-1704
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The Core in Bertrand Oligopoly TU-Games with Transferable Technologies

Aymeric Lardon
Published Online: 2019-06-26 | DOI: https://doi.org/10.1515/bejte-2018-0197

Abstract

In this article we study Bertrand oligopoly TU-games with transferable technologies under the α and β-approaches. We first prove that the core of any game can be partially characterized by associating a Bertrand oligopoly TU-game derived from the most efficient technology. Such a game turns to be an efficient convex cover of the original one. This result implies that the core is non-empty and contains a subset of payoff vectors with a symmetric geometric structure easy to compute. We also deduce from this result that the equal division solution is a core selector satisfying the coalitional monotonicity property on this set of games. Moreover, although the convexity property does not always hold even for standard Bertrand oligopolies, we show that it is satisfied when the difference between the marginal cost of the most efficient firm and the one of the least efficient firm is not too large.

Keywords: Bertrand oligopoly TU-games; transferable technologies; core; convexity property

JEL Classification: C71; D43

References

  • Aumann, R. 1959. “Acceptable Points in General Cooperative n-person Games.” In contributions to the theory of games IV. Annals of Mathematics Studies vol. 40, edited by Luce Tucker. Princeton: Princeton University Press.Google Scholar

  • Bloch, F., and A. van den Nouweland. 2014. “Expectation Formation Rules and the Core of Partition Function Games.” Games and Economic Behavior 88: 538–53.Web of ScienceGoogle Scholar

  • Bondareva, O. N. 1963. “Some Applications of Linear Programming Methods to the Theory of Cooperative Games.” Problemi Kibernetiki 10: 119–39.Google Scholar

  • Chander, P., and H. Tulkens. 1997. “A Core of an Economy with Multilateral Environmental Externalities.” International Journal of Game Theory 26: 379–401.CrossrefGoogle Scholar

  • Driessen, T. S., D. Hou, and A. Lardon. 2010. “Convexity and the Shapley Value in Bertrand Oligopoly TU-games with Shubik’s Demand Functions.” Working paper.

  • Driessen, T. S., and H. I. Meinhardt. 2005. “Convexity of Oligopoly Games Without Transferable Technologies.” Mathematical Social Sciences 50: 102–26.CrossrefGoogle Scholar

  • Ichiishi, T. 1981. “Super-modularity : Applications to Convex Games and to the Greedy Algorithm for lp.” Journal of Economic Theory 25: 283–86.CrossrefGoogle Scholar

  • Lardon, A. 2012. “The γ-core of Cournot Oligopoly Games with Capacity Constraints.” Theory and Decision 72 (3): 387–411.CrossrefWeb of ScienceGoogle Scholar

  • Lardon, A. 2018. “Convexity of Bertrand Oligopoly TU-Games with Differentiated Products (new version).” https://halshs.archives-ouvertes.fr/halshs-00544056v2/document.

  • Lekeas, P. V., and G. Stamatopoulos. 2014. “Cooperative Oligopoly Games with Boundedly Rational Firms.” Annals of Operations Research 223 (1): 255–72.CrossrefWeb of ScienceGoogle Scholar

  • Norde, H., K. H. P. Do, and S. Tijs. 2002. “Oligopoly Games with and without Transferable Technologies.” Mathematical Social Sciences 43: 187–207.CrossrefGoogle Scholar

  • Rulnick, J. M., and L. S. Shapley. 1997. “Convex Covers of Symmetric Games.” International Journal of Game Theory 26: 561–77.CrossrefGoogle Scholar

  • Shapley, L. S. 1955. “Markets as Cooperative Games.” RAND Corporation Paper P-629: 1–5.Google Scholar

  • Shapley, L. S. 1967. “On Balanced Sets and Cores.” Naval Research Logistics Quaterly 14: 453–60.CrossrefGoogle Scholar

  • Shapley, L. S. 1971. “Cores of Convex Games.” International Journal of Game Theory 1: 11–26.CrossrefWeb of ScienceGoogle Scholar

  • Shubik, M. 1980. Market structure and behavior. Cambridge: Harvard University Press.Google Scholar

  • Young, H. P. 1985. “Monotonic Solutions of Cooperatives Games.” International Journal of Game Theory 14 (2): 65–72.CrossrefGoogle Scholar

  • Zhao, J. 1999a. “A Necessary and Sufficient Condition for the Convexity in Oligopoly Games.” Mathematical Social Sciences 37: 189–204.CrossrefGoogle Scholar

  • Zhao, J. 1999b. “A β-Core Existence Result and its Application to Oligopoly Markets.” Games and Economic Behavior 27: 153–68.CrossrefGoogle Scholar

About the article

Published Online: 2019-06-26


Citation Information: The B.E. Journal of Theoretical Economics, Volume 20, Issue 1, 20180197, ISSN (Online) 1935-1704, DOI: https://doi.org/10.1515/bejte-2018-0197.

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