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
Questions (including download problems) about the papers in this series should be directed to Astrid Holm Nielsen ()
Report other problems with accessing this service to Sune Karlsson ().
This page generated on 2024-02-05 17:13:32.