On finite potential games

A linear system, called the potential equation (PE), is presented. It is proved that a finite game is potential if and only if its potential equation has solution. Some properties of the potential equation are obtained. Based on these properties, a closed form solution of the PE is obtained. Moreover, a formula based on the solution of the PE is obtained to calculate the potential function. Finally, it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential. Some interesting examples are presented to illustrate the theoretical results.