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A Necessary and Sufficient Condition for Non-Emptiness of the Core of a Partition Function Form Game

Author

Listed:
  • Takaaki Abe

    (Graduate School of Economics, Waseda University)

  • Yukihiko Funaki

    (Faculty of Political Science and Economics, Waseda University)

Abstract

The purpose of this paper is to provide a necessary and sufficient condition for nonempty core in partition function form games. We generalize the Bondareva-Shapley condition for partition function form games and present the existence conditions for the pessimistic core and the optimistic core. In addition, we study the condition for the core defined by exogenously provided partitions. The balanced collections in partition function form and some applications are also discussed.

Suggested Citation

  • Takaaki Abe & Yukihiko Funaki, 2015. "A Necessary and Sufficient Condition for Non-Emptiness of the Core of a Partition Function Form Game," Working Papers 1502, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1502
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    More about this item

    Keywords

    Cooperative games; Partition function; Core; Externalities;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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