From weighted potential game to weighted harmonic game

Abstract

It was shown that the vector space of finite non-cooperative games can be decomposed into three orthogonal subspaces: the pure potential games (PGs) (P), non-strategic games (N), and pure harmonic games (). This study proposes the concept of weighted harmonic game, and shows that in the aforementioned decomposition the P can be replaced by weighted pure PGs P w , and the can be replaced by WPHGs w . Then the bases for corresponding orthogonal subspaces are presented, respectively. Finally, certain properties of the new decomposed subspaces are investigated.