2013/03/19 by Josep Freixas, Sascha Kurz
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Auction Theory and Applications #Bipartite graph #Combinatorial game theory #Enumeration #Game Theory and Applications #Game Theory and Voting Systems #Rank (graph theory) #Simple (philosophy) #Theory of computation #Type (biology) #Weighted voting #math.CO #msc:91A12 #msc:91A40 #msc:91A80 #msc:91B12
paper · pdf · doi:10.1007/s10479-013-1348-x
26 pages, 2 figures, to appear in Annals of Operations Research
openalex publication_date 2013/03/19 · arxiv created 2013/10/23 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class as well. Second, we focus on the special case of bipartite complete games with minimum, and we compare and rank these games according to the behavior of some efficient power indices of players of type 1 (or of type 2). The main result of this second part establishes all allowable rankings of these games when the Shapley-Shubik power index is used on players of type 1.