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The consistency principle and an axiomatization of the -core

Author

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  • Koji Takamiya

    (Graduate School of Economics and Business Administration, Hokkaido University, Kita9 Nishi7 Sapporo 060-0809 Japan)

Abstract

This paper examines the -core of strategic games by means of the consistency principle. I provide a new definition of a reduced game for strategic games. And I define consistency (CONS) and two forms of converse consistency (COCONS and COCONS*) under this definition of reduced games. Then I axiomatize the -core for families of strategic games with bounded payoff functions by the axioms CONS, COCONS*, weak Pareto optimality (WPO) and one person rationality (OPR). Furthermore, I show that these four axioms are logically independent. In proving this, I also axiomatize the -individually rational solution by CONS, COCONS and OPR for the same families of games. Here the -individually rational solution is a natural extension of the classical `maximin' solution.

Suggested Citation

  • Koji Takamiya, 2001. "The consistency principle and an axiomatization of the -core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 195-207.
    • Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:195-207
    Note: Received: June 1998/Final version: 6 July 2001
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    Cited by:

    1. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.

    More about this item

    Keywords

    axiomatization · reduced game · consistency · converse consistency ·;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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