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The Core And Consistency Properties: A General Characterisation

Author

Listed:
  • YUKIHIKO FUNAKI

    (School of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan)

  • TAKEHIKO YAMATO

    (Department of Value and Decision Science, Graduation School of Decision Science and Technology, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan)

Abstract

In this paper, we unify various axiomatisations of the core ofTUgames by means of consistency with respect to different definitions of reduced games. First, we introduce a general definition of reduced games including the reduced games due to Davis and Maschler (1965), Moulin (1985), and Funaki (1995) as special cases. Then, we provide a general theorem from which the characterisations due to Peleg (1986), Tadenuma (1992), and Funaki (1995) can be obtained. Our general theorem clarifies how the three characterisations of the core differ and are related.

Suggested Citation

  • Yukihiko Funaki & Takehiko Yamato, 2001. "The Core And Consistency Properties: A General Characterisation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 175-187.
    • Handle: RePEc:wsi:igtrxx:v:03:y:2001:i:02n03:n:s0219198901000361
    DOI: 10.1142/S0219198901000361
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    Citations

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    Cited by:

    1. Zhengxing Zou & Rene van den Brink & Yukihiko Funaki, 2020. "Compromising between the proportional and equal division values: axiomatization, consistency and implementation," Tinbergen Institute Discussion Papers 20-054/II, Tinbergen Institute.
    2. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "Axiomatization of an allocation rule for ordered tree TU-games," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 132-140.
    3. Sylvain Béal & Stéphane Gonzalez & Philippe Solal & Peter Sudhölter, 2023. "Axiomatic characterizations of the core without consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 687-701, September.
    4. Dietzenbacher, Bas & Yanovskaya, Elena, 2020. "Antiduality in exact partition games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 116-121.
    5. Bas Dietzenbacher & Peter Sudhölter, 2022. "Hart–Mas-Colell consistency and the core in convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 413-429, June.
    6. Philippe Solal & Sylvain Béal & Sylvain Ferrières & Eric Rémila, 2017. "Axiomatic and bargaining foundation of an allocation rule for ordered tree TU-games," Post-Print halshs-01644811, HAL.
    7. Pérez-Castrillo, David & Sun, Chaoran, 2021. "Value-free reductions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 543-568.
    8. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
    9. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    10. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
    11. René Brink & Youngsub Chun & Yukihiko Funaki & Boram Park, 2016. "Consistency, population solidarity, and egalitarian solutions for TU-games," Theory and Decision, Springer, vol. 81(3), pages 427-447, September.
    12. Yasushi Agatsuma & Yukihiko Funaki & Koji Yokote, 2017. "Random reduction consistency of the Weber set, the core and the anti-core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 389-405, June.
    13. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2017. "Coincidence of the Shapley value with other solutions satisfying covariance," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 1-9.

    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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