  By resorting to the vector space structure of finite games, skew-symmetric
games (SSGs) are proposed and investigated as a natural subspace of finite
games. First of all, for two player games, it is shown that the skew-symmetric
games form an orthogonal complement of the symmetric games. Then for a general
SSG its linear representation is given, which can be used to verify whether a
finite game is skew-symmetric. Furthermore, some properties of SSGs are also
obtained in the light of its vector subspace structure. Finally, a
symmetry-based decomposition of finite games is proposed, which consists of
three mutually orthogonal subspaces: symmetric subspace, skew-symmetric
subspace and asymmetric subspace. An illustrative example is presented to
demonstrate this decomposition.

Computer Science and Game Theory;Combinatorics