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An algorithm is proposed to verify whether a finite game is a weightedpotential game (WPG) without pre-knowledge on its weights. Then the algorithmis also applied to find the closest WPG for a given finite game. The conceptand criterion of near weighted potential games (NWPGs) are given, indicatingthe evolutionary equivalence between a finite game and its closest WPG. Basedon this, a method is proposed for replacing PGs by NWPGs in game theoreticcontrol, which improved the applicability of PG-based optimization.

Weighted and Near Weighted Potential Games with Application to Game Theoretic Control