A Generalization of Weighted Congestion Game and its Nash Equilibrium Seeking

In this paper, a variation of the congestion situation and the associated weighted congestion games are considered. By using semi-tensor product of matrices, the structure and algebraic representation of resulted game are investigated. The associated weighted congestion game is also proved to be a weighted potential game. Furthermore, an algorithm is provided to search the pure Nash equilibrium of resulted games. Finally, an example is studied to illustrative the effectiveness of our new results.