Abstract
This paper studies the verification of multi-potential games with a given partition, and proposes a kind of multi-potential equation based on semi-tensor product of matrices. Firstly, the basis of each player’s potential function is constructed, based on which, a new formula is established for the calculation of each player’s potential function. Secondly, a new potential equation is proposed for the verification of potential games via each player’s potential function. Using the new potential equation, a kind of multi-potential equation is constructed for the verification of multi-potential games with a given partition. It is proved that a finite game is a multi-potential game with a given partition if and only if the multi-potential equation has solution. In addition, all possible potential functions are obtained for each group of the partition. An illustrative example is worked out to show the effectiveness of the obtained new results.
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