On the accessibility of core-extensions

Sengupta and Sengupta (1996) study the accessibility of the core of a TU game and show that the core, if non-empty, can be reached from any non-core allocation via a finite sequence of successive blocks. This paper complements the result by showing that when the core is empty, a number of non-empty...

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Bibliographic Details
Published in:Games and economic behavior 2012-03, Vol.74 (2), p.687-698
Main Author: Yang, Yi-You
Format: Article
Language:English
Subjects:
Accessibility
Allocations
Allocative efficiency
Coalitions
Cooperation
Core
Core-extensions
Economic models
Game theory
Stochastic processes
Studies
Utility theory
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Summary:Sengupta and Sengupta (1996) study the accessibility of the core of a TU game and show that the core, if non-empty, can be reached from any non-core allocation via a finite sequence of successive blocks. This paper complements the result by showing that when the core is empty, a number of non-empty core-extensions, including the least core and the weak least core (Maschler et al., 1979), the positive core (Orshan and Sudhölter, 2001) and the extended core (Bejan and Gómez, 2009), are accessible in a strong sense, namely each allocation in each of the foregoing core-extensions can be reached from any allocation through a finite sequence of successive blocks. ► An accessible allocation exists if and only if the core is empty or a singleton. ► The set of accessible allocations, if non-empty, contains the (weak) least core. ► The set of accessible allocations, if non-empty, contains the extended core. ► The nucleolus of an N-monotonic unbalanced game is an accessible allocation.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2011.08.007