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Accessible outcomes versus absorbing outcomes

  • Yang, Yi-You

(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.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 62 (2011)
Issue (Month): 1 (July)
Pages: 65-70

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Handle: RePEc:eee:matsoc:v:62:y:2011:i:1:p:65-70
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. 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.
  2. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
  3. 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.
  4. 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.
  5. Laszlo.A.Koczy, 2005. "The Core Can Be Accessed with a Bounded Number of Blocks," IEHAS Discussion Papers 0512, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  6. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
  7. 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 347-59, May.
  8. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
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