Paper Info
Title
Complementary Weighted Multiple Majority Games
Abstract
In this paper, we introduce a new family of simple games, which is referred to as the complementary weighted multiple majority game. For the two dimensional case, we prove that there are at most n+1 minimal winning coalitions (MWC for short), where n is the number of players. An algorithm for computing all the MWCs is presented, with a running time of O(nlog n). Computing the main power indices, i.e. Shapley-Shubik index, Banzhaf index, Holler-Packel index, and Deegan-Packel index, can all be done in polynomial time. Still for the two dimensional case, we show that local monotonicity holds for all of the four power indices. We also define a new kind of stability: the C-stability. Assuming that allocation of the payoff among the winning coalition is proportional to players' powers, we show that C-stable coalition structures are those that contain an MWC with the smallest sum of powers. Hence, C-stable coalition structures can be computed in polynomial times.
Year
Venue
Keywords
2009
Clinical Orthopaedics and Related Research
c-stability,simple games,minimal winning coalitions.,polynomial times. keywords: complementary weighted multiple majority games,power indices,indexation,polynomial time,sums of powers
Field
DocType
Volume
Discrete mathematics,Algebra,Mathematics
Journal
abs/0904.2
Citations 
PageRank 
References 
0
0.34
8
Authors
2
Name
Order
Citations
PageRank
Zhigang Cao11083123.08
Xiaoguang Yang2302.99