Isbell, J. R. A class of simple games. (English) Zbl 0083.14301 Duke Math. J. 25, 423-439 (1958). H. M. Gurk and the author have shown [Ann. Math. Stud. 40, 247–265 (1958; Zbl 0085.13105)] that every strong simple game (for definitions, see the review of the author’s paper [Math. Student 25, 123–128 (1958; Zbl 0083.14204)] above) has at least as many minimal winning sets as non-dummy players. In the present paper all cases of equality are listed. They are a seven-player projective game, and an infinite set given in another paper by the same author [Q. J. Math., Oxf. II. Ser. 7, 183–187 (1956; Zbl 0073.13401)]. Reviewer: S. Vajda Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 83 Documents MSC: 91A12 Cooperative games Keywords:minimal winning sets; strong simple games; seven-player projective game; majority games Citations:Zbl 0085.13105; Zbl 0083.14204; Zbl 0073.13401 PDF BibTeX XML Cite \textit{J. R. Isbell}, Duke Math. J. 25, 423--439 (1958; Zbl 0083.14301) Full Text: DOI OpenURL