On Finite Weighted Potential Game

This work addresses the finite weighted potential game, where we design a method to verify whether the finite weighted game is potential or not. Firstly, we analyze the inherent relation between a finite potential game and weighted potential game. Secondly, for a finite weighted game, we use a function and present some properties of the semi-tensor product. Finally, we establish a weighted potential equation, where the weighted game is potential game if and only if the equation has a solution. Moreover, we give some examples to illustrate the theoretical results.