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On equivalence of state-based potential games

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Abstract

In this paper, we explore state-based potential games using the semi-tensor product of matrices. First, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

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Acknowledgements

This work was supported by Natural Science Foundation of Hebei Province (Grant No. F2021202032) and Graduate Innovation Funding Program of Hebei Province (Grant No. CXZZSS2023033).

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Authors and Affiliations

  1. Institute of Mathematics, School of Science, Hebei University of Technology, Tianjin, 300401, China

    Han Wu & Jinhuan Wang

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  1. Han Wu
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  2. Jinhuan Wang
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Correspondence to Jinhuan Wang.

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Wu, H., Wang, J. On equivalence of state-based potential games. Sci. China Inf. Sci. 67, 162205 (2024). https://doi.org/10.1007/s11432-023-3995-5

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  • DOI: https://doi.org/10.1007/s11432-023-3995-5

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