A class of simple games (Q770599)

\textit{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)].