Decomposed Subspaces of Ex-Ante Agent Games

In this paper, the orthogonal decomposition of ex-ante agent games is studied by using the semi-tensor product (STP). Firstly, by analyzing game condition of the ex-ante agent game, the subspace of potential game and non-strategic space are obtained. Then, using the orthogonal projection, the projection of the pure potential subspace
$\mathcal{P}$
, the non-strategic subspace
$\mathcal{N}$
, and the pure harmonic subspace
$\mathcal{H}$
are calculated. Finally, the theoretical results are applied to find near-potential games.