Core stability and other applications of minimal balanced collections

Peter Sudhölter, Michel Grabisch and Dylan Laplace Mermoud

No 4/2022, Discussion Papers on Economics from University of Southern Denmark, Department of Economics

Abstract: We describe algorithms and their implementations as computer programs derived from several theoretical results of the theory of cooperative transferable utility (TU) games. We show how to use Peleg’s well-known inductive method to explicitly compute all minimal balanced collections of coalitions. The described method is of independent interest and applied in the implementations of (a) the Bondareva-Shapley Theorem, which allows checking whether a TU game is balanced, i.e., has a non-empty core, and (b) a recent result of the second and third author that provides a sufficient and necessary condition for the stability of the core, which allows checking whether a balanced TU game has a core that is a von Neumann-Morgenstern stable set.

Keywords: Core; stable set; minimal balanced collections; cooperative game. (search for similar items in EconPapers)
JEL-codes: C44 C71 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2022-06-08
New Economics Papers: this item is included in nep-gth and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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