2017/01/24 by Daizhan Cheng, Ting Liu, Cheng, Daizhan +1
Computer Science · Decision Sciences · Engineering · #Artificial Immune Systems Applications #Artificial Intelligence in Games #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1701.06807
openalex publication_date 2017/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the symmetry, described as the action of symmetric group on payoff functions, is converted into the product of permutation matrices with structure vectors of payoff functions. Using the linear representation of the symmetric group in structure vectors, the algebraic conditions for the ordinary, weighted, renaming and name-irrelevant symmetries are obtained respectively as the invariance under the corresponding linear representations. Secondly, using the linear representations the relationship between symmetric games and potential games is investigated. This part is mainly focused on Boolean games. An alternative proof is given to show that ordinary, renaming and weighted symmetric Boolean games are also potential ones under our framework. The corresponding potential functions are also obtained. Finally, an example is given to show that some other Boolean games could also be potential games.