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Stability and largeness of core for symmetric games

Author

Listed:
  • Amit K. Biswas

    (Indian Statistical Institute, 110, Nelson Manickam Road, Aminjikarai, Madras 600029, India Indian Statistical Institute, 8th Mile Mysore Road, R.V. College Post, Banglore 560059, India Indian Statistical Institute, Math - Stat Division, 7, S.J.S. Sansanwal Marg, New Delhi 110016, India)

  • G. Ravindran

    (Indian Statistical Institute, 110, Nelson Manickam Road, Aminjikarai, Madras 600029, India Indian Statistical Institute, 8th Mile Mysore Road, R.V. College Post, Banglore 560059, India Indian Statistical Institute, Math - Stat Division, 7, S.J.S. Sansanwal Marg, New Delhi 110016, India)

  • T. Parthasarathy

    (Indian Statistical Institute, 110, Nelson Manickam Road, Aminjikarai, Madras 600029, India Indian Statistical Institute, 8th Mile Mysore Road, R.V. College Post, Banglore 560059, India Indian Statistical Institute, Math - Stat Division, 7, S.J.S. Sansanwal Marg, New Delhi 110016, India)

Abstract

Largeness of the core is sufficient for stability of the core. In general the necessity is not known. In this paper we answer affirmatively the necessity for symmetric games. We also prove its equivalence to n specified vectors being imputations and also to the convexity of the lower boundary of the set of all acceptable pay-off vectors of the game. In this paper we establish the equivalence of a condition given by Shapley to the newly evolved condition, thereby give an alternate proof to Shapley's condition.

Suggested Citation

  • Amit K. Biswas & G. Ravindran & T. Parthasarathy, 2000. "Stability and largeness of core for symmetric games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 11-22.
    • Handle: RePEc:spr:jogath:v:29:y:2000:i:1:p:11-22
    Note: Received: January 1997/final version: March 1999
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    Citations

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    Cited by:

    1. Hirai, Toshiyuki & Watanabe, Naoki, 2018. "von Neumann–Morgenstern stable sets of a patent licensing game: The existence proof," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 1-12.
    2. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    3. F. Martínez-de-Albéniz & Carles Rafels, 2007. "Minimal large sets for cooperative games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 242-255, December.
    4. van Velzen, Bas & Hamers, Herbert & Solymosi, Tamas, 2008. "Core stability in chain-component additive games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 116-139, January.
    5. Biswas, Amit K. & Parthasarathy, T. & Ravindran, G., 2001. "Stability and Largeness of the Core," Games and Economic Behavior, Elsevier, vol. 34(2), pages 227-237, February.
    6. K. C. Sivakumar & M. S. Gowda & G. Ravindran & Usha Mohan, 2020. "Preface: International conference on game theory and optimization, June 6–10, 2016, Indian Institute of Technology Madras, Chennai, India," Annals of Operations Research, Springer, vol. 287(2), pages 565-572, April.

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