Accessible outcomes versus absorbing outcomes

Kóczy and Lauwers (2004, 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 reach...

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Bibliographic Details
Published in:Mathematical social sciences 2011-07, Vol.62 (1), p.65-70
Main Author: Yang, Yi-You
Format: Article
Language:English
Subjects:
Coalitions
Game theory
Pay-off
Utility functions
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Summary:Kóczy and Lauwers (2004, 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. ► The coalition structure core can be reached from any outcome in quadratic time. ► The set of accessible outcomes, if non-empty, is a minimal dominant set. ► A cohesive game possesses an absorbing outcome or an accessible outcome. ► The minimal dominant set of a cohesive game can be reached in linear time.
ISSN:0165-4896
1879-3118
DOI:10.1016/j.mathsocsci.2011.04.008