Béal, Sylvain and Rémila, Eric and Solal, Philippe (2011): On the number of blocks required to access the coalition structure core.

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Abstract
This article shows that, for any transferable utility game in coalitional form with nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to (n*n+4n)/4, where n is the cardinality of the player set. This number considerably improves the upper bound found so far by Koczy and Lauwers (2004).
Item Type:  MPRA Paper 

Original Title:  On the number of blocks required to access the coalition structure core 
Language:  English 
Keywords:  coalition structure core; excess function; payoff configuration; outsider independent domination. 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games 
Item ID:  29755 
Depositing User:  Sylvain Béal 
Date Deposited:  04. Apr 2011 20:50 
Last Modified:  15. Feb 2013 06:24 
References:  [1] R. J. Aumann, "Some nonsuperadditive games, and their Shapley value, in the Talmud", International Journal of Game Theory 39 (2010), pp. 3–10. [2] S. Béal, E. Rémila and P. Solal, "On the number of blocks required to access the core", MPRA Paper No. 26578, 2010. [3] D. B. Gillies, "Some theorems on nperson games", Ph.D. dissertation, Princeton University, Department of Mathematics, 1953. [4] J. Greenberg, "Coalition structures", ch. 37 in Handbook of Game Theory with Economic Applications, vol II, (R.J. Aumann and S. Hart eds.), pp. 1305–1307, Elsevier, Amsterdam, 1994. [5] L. Kóczy, "The core can be accessed with a bounded number of blocks", Journal of Mathematical Economics 43 (2006), pp. 56–64. [6] L. Kóczy and L. Lauwers, "The coalition structure core is accessible", Games and Economic Behavior 48 (2004), pp. 86–93. [7] A. Sengupta and K. Sengupta, "Viable proposals", International Economic Review 35 (1994), pp. 347–359. [8] A. Sengupta and K. Sengupta, "A property of the core", Games and Economic Behavior 12 (1996), pp. 266–273. [9] L. S. Shapley, "Cores of convex games", International Journal of Game Theory (1971), 1, pp. 11–26. [10] P. P. Shenoy, "On coalition formation: a gametheoretical approach", International Journal of Game Theory 8 (1979), pp. 133–164. [11] Y.Y. Yang, "On the accessibility of the core", Games and Economic Behavior 69 (2010), pp. 194–199. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/29755 