Verification of coset weighted potential game and its application to optimisation of multi-agent systems

Abstract

In this paper, we propose an algorithm to verify whether a finite game is a coset weighted potential game (WPG) without pre-knowledge on its coset weights. This algorithm can also provide a recursive method to calculate the unknown coset weights. Then we give the concept of near coset WPGs based on evolutionary equivalence between two finite games, and its algebraic verification is obtained. Finally, the application of near coset WPGs to game-theoretical optimisation of multi-agent systems is discussed, which can improve the applicability of potential games in multi-agent optimisation problems.

Keywords:

• Coset weighted potential game
• near coset weighted potential game
• evolutionary equivalence
• semi-tensor product of matrices
• game-theoretical optimisation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundation of China under grants 61903236, 62073202 and 61803240.