{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:11:08Z","timestamp":1760242268388,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,2,28]],"date-time":"2017-02-28T00:00:00Z","timestamp":1488240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>We study the class of directed simple games, assuming that only integer solutions are admitted; i.e., the players share a resource that comes in discrete units. We show that the integer nucleolus\u2014if nonempty\u2014of such a game is composed of the images of a particular payoff vector under all symmetries of the game. This payoff vector belongs to the set of integer imputations that weakly preserve the desirability relation between the players. We propose an algorithm for finding the integer nucleolus of any directed simple game with a nonempty integer imputation set. The algorithm supports the parallel execution of multiple threads in a computer application. We also consider the integer prenucleolus and the class of directed generalized simple games.<\/jats:p>","DOI":"10.3390\/g8010016","type":"journal-article","created":{"date-parts":[[2017,2,28]],"date-time":"2017-02-28T10:57:52Z","timestamp":1488279472000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm"],"prefix":"10.3390","volume":"8","author":[{"given":"Reiner","family":"Wolff","sequence":"first","affiliation":[{"name":"Department of Economics, University of Fribourg, 1700 Fribourg, Switzerland"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1137\/0117107","article-title":"The Nucleolus of a Characteristic Function Game","volume":"17","author":"Schmeidler","year":"1969","journal-title":"SIAM J. Appl. 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