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Structure of finite games with symmetric potential functions
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DOI：10.1007/s11432-024-4790-5.png)
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Abstract
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The structure of finite games with symmetric potential functions is investigated in this paper. First, by constructing a basis of symmetric functions, a necessary and sufficient condition is presented to verify whether a finite game has symmetric potential functions. Then, a basis of the subspace of finite games with symmetric potential functions is provided. Next, the symmetric potential game is studied. By proving the symmetry of the potential function, a linear system is also presented for the verification of symmetric potential games, as well as a basis. Finally, as an application of the obtained results, the optimization of quasi-symmetric spatial games is considered. A sufficient condition for the utility design is given to turn the spatial game into a weighted potential game with the preassigned objective function as the potential function.
Keywords:
potential game
symmetric potential function
symmetric potential game
quasi-symmetric spatial game
utility design
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