Scandinavian Working Papers in Economics
Discussion Papers on Economics,
University of Southern Denmark, Department of Economics
No 4/2022: Core stability and other applications of minimal balanced collections
Peter Sudhölter (), Michel Grabisch and Dylan Laplace Mermoud ()
Additional contact information
Peter Sudhölter: Department of Economics, Postal: Department of Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Michel Grabisch: Paris School of Economics, Université Paris, Postal: Paris School of Economics, Université Paris 1 Panthéon-Sorbonne, 75231 Paris, France
Dylan Laplace Mermoud: Paris School of Economics, Université Paris, Postal: Paris School of Economics, Université Paris 1 Panthéon-Sorbonne, 75231 Paris, France
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.
Language: English
19 pages, June 8, 2022
Full text files
dpe04_2022.pdf?rev=-...11B213F25C8AF06FBF78Full text
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