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(Average-) Convexity Of Common Pool And Oligopoly Tu-Games

Author

Listed:
  • THEO S. H. DRIESSEN

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

  • HOLGER MEINHARDT

    (Projekt Umweltgemeingüter, Lehrstuhl für Volkswirtschaftslehre 3, Postfach 69 80, Universität Karlsruhe, Zirkel 2, D-76128 Karlsruhe, Germany)

Abstract

The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexity, however, fails whenever cost functions are arbitrary. We present sufficient conditions involving the cost functions (like weakly decreasing marginal costs as well as weakly decreasing average costs) and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function.

Suggested Citation

  • Theo S. H. Driessen & Holger Meinhardt, 2001. "(Average-) Convexity Of Common Pool And Oligopoly Tu-Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 141-158.
    • Handle: RePEc:wsi:igtrxx:v:03:y:2001:i:02n03:n:s0219198901000336
    DOI: 10.1142/S0219198901000336
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    Citations

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    Cited by:

    1. Axel Ostmann & Holger Meinhardt, 2007. "Non-binding agreements and fairness in commons dilemma games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(1), pages 63-96, March.
    2. 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.

    More about this item

    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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