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On The Supermodularity Of Homogeneous Oligopoly Games

Author

Listed:
  • THEO DRIESSEN

    (Faculty of Mathematical Sciences, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands)

  • HOLGER MEINHARDT

    (Institute of Operations Research, University of Karlsruhe, Englerstr. 11, Building: 11.40, D-76128 Karlsruhe, Germany)

Abstract

The main purpose is to prove the supermodularity (convexity) property of a cooperative game arising from an economical situation. The underlying oligopoly situation is based on a linear inverse demand function as well as linear cost functions for the participating firms. The characteristic function of the so-called oligopoly game is determined by maximizing, for any cartel of firms, the net profit function over the feasible production levels of the firms in the cartel, taking into account their individual capacities of production and production technologies. The (rather effective) proof of the supermodularity of the characteristic function of the oligopoly game relies on the use of maximizers for the relevant maximization problems. A similar proof technique will be reviewed for a related cooperative oligopoly game arising from a slightly modified oligopoly situation where the production technology of the cartel is determined by the most efficient member firm.

Suggested Citation

  • Theo Driessen & Holger Meinhardt, 2010. "On The Supermodularity Of Homogeneous Oligopoly Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 309-337.
    • Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002702
    DOI: 10.1142/S0219198910002702
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    Cited by:

    1. Meinhardt, Holger Ingmar, 2020. "On the Replication of the Pre-Kernel and Related Solutions," MPRA Paper 102676, University Library of Munich, Germany.

    More about this item

    Keywords

    Cooperative game; oligopoly TU-game; convexity; supermodularity; cartel; 91A12; 91A40; C71; D43; L13;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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