Accessibility and stability of the coalition structure core

Sylvain Béal, Eric Rémila and Philippe Solal

Mathematical Methods of Operations Research, 2013, vol. 78, issue 2, 187-202

Abstract: This article shows that, for any transferable utility game in coalitional form with a 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 $$(n^2+4n)/4$$ , where $$n$$ is the cardinality of the player set. This number improves the upper bounds found so far. We also provide a sufficient condition for the stability of the coalition structure core, i.e. a condition which ensures the accessibility of the coalition structure core in one step. On the class of simple games, this sufficient condition is also necessary and has a meaningful interpretation. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Coalition structure core; Excess function; Payoff configuration; Outsider independent domination; Accessibility; Core stability; Simple games; Veto player; 91A12 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00186-013-0439-4

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