On Characterizations of Potential and Ordinal Potential Games
<|reference_start|>On Characterizations of Potential and Ordinal Potential Games: This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with multi-dimensional action spaces, which require differentiable cost functions. Then, we provide a necessary and sufficient conditions for a game to have a potential function by investigating the structure of a potential function in terms of the players' cost differences, as opposed to differentials. This condition provides a systematic way for construction of a potential function, which is applied to network congestion games, as an example. Finally, we provide some sufficient conditions for a game to be ordinal potential and generalized ordinal potential.<|reference_end|>
@article{arefizadeh2024on,
    title={On Characterizations of Potential and Ordinal Potential Games},
    author={Sina Arefizadeh, Angelia Nedich, Gautam Dasarathy},
    journal={arXiv preprint arXiv:2405.06253},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06253},
    primaryClass={cs.GT math.OC}
}