Nash equilibria in nonsymmetric singleton congestion games with exact partition

We define a new class of games, which we qualify as congestion games with exact partition. These games constitute a subfamily of singleton congestion games for which the players are restricted to choose only one strategy, but they each possess their own utility function. The aim of this paper is to develop a method leading to an easier identification of all Nash equilibria in this kind of congestion games. We also give a new proof establishing the existence of a Nash equilibrium in this type of games without invoking the potential function or the finite best-reply property.