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| STP-based verification of extended finite multi-potential games |
| ZhipengZhang1,HaotianPeng2,JianboSong1,ZengqiangChen3 |
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| (1 School of Artificial Intelligence, Tiangong University, Tianjin 300387, China;2 School of Control Science and Engineering, Tiangong University, Tianjin 300387, China;3 College of Artificial Intelligence, Nankai University, Tianjin 300350, China) |
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| 摘要: |
| Potential games (PG) have attracted the attention of many researchers because of its excellent properties and multi-PG are more flexible and extensible, which greatly improve the application range of PG. Consider that weights and states to each player are common and practical in many application scenarios, and in this paper, by introducing weight value and state into multi-PG, q-weighted PG and q-state PG are systematically discussed and analyzed to expand the types of PG, respectively. First, using semi-tensor product of matrices (STP), a matrix approach to the modeling of weighted PG is nvestigated, and the verification method of weighted PG is proposed by defining three matrices, and the problem of how to detect weighted PG can be transformed to solve an algebraic equation, which is composed of the above three matrices. Next, by bringing weight values into multi-PG and detecting the weighted PG for each group, the verification method is extended to the q-weighted PG. Second, the model of state-based PG is constructed, and the problem of how to detect state-based PG can be transformed to solve another algebraic equation, which is seen as an extension of the verification method of weighted PG. Subsequently,
the verification of q-state PG is discussed. Finally, we use two examples to demonstrate the validation of obtained results. |
| 关键词: Semi-tensor product of matrices · Multi-potential games · Weighted logic system · Linear algebraic equation |
| DOI：https://doi.org/10.1007/s11768-025-00255-9 |
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| 基金项目:This work was partially supported by the National Natural Science Foundation of China Grant No. 62203328. |
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| STP-based verification of extended finite multi-potential games |
| Zhipeng Zhang1,Haotian Peng2,Jianbo Song1,Zengqiang Chen3 |
| (1 School of Artificial Intelligence, Tiangong University, Tianjin 300387, China;2 School of Control Science and Engineering, Tiangong University, Tianjin 300387, China;3 College of Artificial Intelligence, Nankai University, Tianjin 300350, China) |
| Abstract: |
| Potential games (PG) have attracted the attention of many researchers because of its excellent properties and multi-PG are more flexible and extensible, which greatly improve the application range of PG. Consider that weights and states to each player are common and practical in many application scenarios, and in this paper, by introducing weight value and state into multi-PG, q-weighted PG and q-state PG are systematically discussed and analyzed to expand the types of PG, respectively. First, using semi-tensor product of matrices (STP), a matrix approach to the modeling of weighted PG is nvestigated, and the verification method of weighted PG is proposed by defining three matrices, and the problem of how to detect weighted PG can be transformed to solve an algebraic equation, which is composed of the above three matrices. Next, by bringing weight values into multi-PG and detecting the weighted PG for each group, the verification method is extended to the q-weighted PG. Second, the model of state-based PG is constructed, and the problem of how to detect state-based PG can be transformed to solve another algebraic equation, which is seen as an extension of the verification method of weighted PG. Subsequently,
the verification of q-state PG is discussed. Finally, we use two examples to demonstrate the validation of obtained results. |
| Key words: Semi-tensor product of matrices · Multi-potential games · Weighted logic system · Linear algebraic equation |
