  In this paper, we introduce a simplicial complex representation for finite
non-cooperative games in the strategic form. The covering space of the
simplicial game complex is introduced and we show that the covering complex is
a powerful tool to find Nash Equilibrium simplices. This representation allows
us to model the cost functions of a game as a weight number on a dual vertex of
the strategy situation in some stars. It yields a canonical direct sum
decomposition of an arbitrary game into three components, as the potential,
harmonic and nonstrategic components.
