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Fixed Point Approaches to the Proof of the Bondareva-Shapley Theorem

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  • Jean Guillaume Forand

    (Department of Economics, University of Waterloo)

  • Metin Uyanik

    (School of Economics, University of Queensland)

Abstract

We provide two new proofs of the Bondareva-Shapley theorem, which states that the core of a transferable utility cooperative is nonempty if and only if the game is balanced. Both proofs exploit the fixed points of self-maps of the set of imputations, applying elementary existence arguments typically associated with noncooperative games to cooperative games.

Suggested Citation

  • Jean Guillaume Forand & Metin Uyanik, 2017. "Fixed Point Approaches to the Proof of the Bondareva-Shapley Theorem," Working Papers 1706, University of Waterloo, Department of Economics, revised Nov 2017.
    • Handle: RePEc:wat:wpaper:1706
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    References listed on IDEAS

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    1. Zhou, Lin, 1994. "A Theorem on Open Coverings of a Simplex and Scarf's Core Existence Theorem through Brouwer's Fixed Point Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 473-477, May.
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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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