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Accessible outcomes versus absorbing outcomes

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  • Yang, Yi-You

Abstract

(Kóczy and Lauwers, 2004) and (Kóczy and Lauwers, 2007) show that the collection of absorbing outcomes, i.e., the coalition structure core, of a TU game, if non-empty, is a minimal dominant set. The paper complements the result in two respects. First, it is shown that the coalition structure core, if non-empty, can be reached from any outcome via a sequence of successive blocks in quadratic time. Second, we observe that an analogous result holds for accessible outcomes, namely, the collection of accessible outcomes, if non-empty, is a minimal dominant set. Moreover, we give an existence theorem for accessible outcomes, which implies that the minimal dominant set of a cohesive game is exactly the coalition structure core or the collection of accessible outcomes, either of which can be reached from any outcome in linear time.

Suggested Citation

  • Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
  • Handle: RePEc:eee:matsoc:v:62:y:2011:i:1:p:65-70
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    References listed on IDEAS

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    1. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
    2. Sengupta, Abhijit & Sengupta, Kunal, 1994. "Viable Proposals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(2), pages 347-359, May.
    3. Koczy, Laszlo A., 2006. "The core can be accessed with a bounded number of blocks," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 56-64, December.
    4. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "On the number of blocks required to access the core," MPRA Paper 26578, University Library of Munich, Germany.
    5. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    6. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    7. Greenberg, Joseph, 1994. "Coalition structures," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 37, pages 1305-1337 Elsevier.
    8. Luc Lauwers, 2002. "A Note on Viable Proposals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1369-1371, November.
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    Cited by:

    1. repec:spr:grdene:v:27:y:2018:i:3:d:10.1007_s10726-018-9570-1 is not listed on IDEAS
    2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2013. "An optimal bound to access the core in TU-games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 1-9.
    3. Péter Szikora, 2013. "Introduction into the literature of cooperative game theory with special emphasis on dynamic games and the core," Proceedings- 11th International Conference on Mangement, Enterprise and Benchmarking (MEB 2013), Óbuda University, Keleti Faculty of Business and Management.
    4. 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.
    5. Péter Biró & Gethin Norman, 2013. "Analysis of stochastic matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1021-1040, November.
    6. repec:spr:compst:v:78:y:2013:i:2:p:187-202 is not listed on IDEAS

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