access icon free Linear representation of symmetric games

Using the linear representation of symmetric group in the structure vector of finite games as its representation space, the inside structures of several kinds of symmetric games are investigated. First of all, the symmetry, described as the action of symmetric group on payoff functions, is converted to the product of permutation matrices with structure vectors of payoff functions. Second, in the light of the linear representation of the symmetric group in structure vectors, the algebraic conditions for the ordinary, weighted, renaming and name-irrelevant symmetries are obtained as the invariance under the corresponding linear representations. The semi-tensor product of matrices is a fundamental tool in this approach.

Inspec keywords: game theory; matrix algebra; tensors; group theory; vectors

Other keywords: finite games; symmetric games linear representation; structure vector; algebraic conditions; semitensor product; renaming symmetry; permutation matrices; name-irrelevant symmetry; ordinary symmetry; payoff functions; symmetric group; weighted symmetry

Subjects: Algebra; Algebra; Algebra; Statistics; Game theory; Group theory; Algebra, set theory, and graph theory; Probability theory, stochastic processes, and statistics; Game theory

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