Graphs, Topologies and simple games

Abstract

We study the existence of connected coalitions in a simple game restricted

by a partia/ order. First, we define a topology compatible with the par- tia/ order in the set of players. Second, we prove some properties of the

covering and comparability graphs of a finite poset. Finally, we analize

the core and obtain sufficient conditions for the existence of winning coa- litions such that contains dominant players in simple games restricted by

the connected subspaces of a finite topological space.