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Public goods game with umpire supervision: Based on complex networks and birandom geometric graph |
| Yanzhe Huang(黄彦喆)1,2, Lilan Tu(涂俐兰)1,2,†, Xianjia Wang(王先甲)3, Yuchen Shao(邵雨晨)1,2, Xiaoyang Wang(王晓阳)1,2, and Ye Pan(潘烨)1,2 |
1 Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China;
2 College of Science, Wuhan University of Science and Technology, Wuhan 430065, China;
3 Economics and Management School, Wuhan University, Wuhan 430072, China |
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Abstract Using complex networks and the birandom geometric graph (BRGG) model, we first propose a construction algorithm for a two-layer network with umpire supervision (i.e., US-BRGBA). Subsequently, we introduce a reward-punishment mechanism imposed by umpires on players while considering both fair and corrupt umpires, thereby presenting the US-BRGBA game model with umpire supervision. Further, the feasibility and effectiveness of the proposed US-BRGBA model based on Monte Carlo (MC) simulations are verified, as well as the influence on players’ cooperative behaviors arising from umpires’ spatial distribution, the fraction of fair umpires, the reward value, the fine value, and the bribe value. Abundant simulations demonstrate that the US-BRGBA model promotes cooperation significantly. Additionally, the spatial distribution patterns of umpires do not consistently yield uniform effects on promoting cooperation, as their influences are contingent upon the fraction of fair umpires and the magnitude of the synergy factor. In resource-abundant regions, corruption does not block cooperative behaviors. Meanwhile, the introduction of umpires consistently facilitates cooperation, even in scenarios where all umpires exhibit corrupt behavior. Further, compared with the reward value and fine value, the cooperative behavior in the US-BRGBA game model is more sensitive to the bribe value.
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Received: 27 August 2025
Revised: 10 October 2025
Accepted manuscript online: 17 October 2025
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PACS:
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02.10.Ox
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(Combinatorics; graph theory)
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02.50.Le
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(Decision theory and game theory)
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02.70.Uu
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(Applications of Monte Carlo methods)
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02.70.-c
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(Computational techniques; simulations)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 72031009). |
Cite this article:
Yanzhe Huang(黄彦喆), Lilan Tu(涂俐兰), Xianjia Wang(王先甲), Yuchen Shao(邵雨晨), Xiaoyang Wang(王晓阳), and Ye Pan(潘烨) Public goods game with umpire supervision: Based on complex networks and birandom geometric graph 2026 Chin. Phys. B 35 080201
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[1] Chaudhuri A 2011 Exp. Econ. 14 47
[2] Nowak M A 2006 Science 314 1560
[3] Glynatsi N E, Akin E, Nowak M A and Hilbe C 2024 Proc. Natl. Acad. Sci. USA 121 e2420125121
[4] Lange T Z and Waring T M 2025 Evol. Hum. Sci. 7 e12
[5] Xia C, Wang J, Perc M, Wang Z 2023 Phys. Life Rev. 46 8
[6] Wang J and Xia C 2023 Europhys. Lett. 141 21001
[7] Williams G C 2001 Sci. Aging Knowledge Environ 2001 cp13
[8] Michod R E 2000 Darwinian dynamics: evolutionary transitions in fitness and individuality (Princeton University Press)
[9] Traulsen A and Nowak M A 2006 Proc. Natl. Acad. Sci. USA 103 10952
[10] Szabo G and Szolnoki A 2009 Phys. Rev. E 79 016106
[11] Ohtsuki H, Hauert C, Lieberman E and Nowak M A 2006 Nature 441 502
[12] Jun T and Sethi R 2007 J. Evol. Econ. 17 623
[13] Wang Z, Xu Z J and Zhang L Z 2010 Chin. Phys. B 19 110201
[14] Quan J, Chu Y Q, Liu W, Wang X J and Yang X K 2018 Chin. Phys. B 27 060203
[15] Botta R, Blanco G and Schaerer C E 2024 Sci. Rep. 14 7903
[16] Sun X, Li M, Kang H, Shen Y and Chen Q 2023 Appl. Math. Comput. 445 127853
[17] Sun X P, Bi Y Z, Kang H W, Shen Y and Chen Q Y 2024 Chin. Phys. B 33 090204
[18] Yue L, Zhang H, Sun Y, An T and Wang J 2025 iScience 28 111813
[19] Quan J, Zhang M, Zhou Y, Wang X and Yang J B 2019 J. Stat. Mech. Theory Exp. 2019 103405
[20] Pancotto F, Righi S and Takacs K 2023 Theory Decis. 95 405
[21] Haq H, Schimit P H T and Broom M 2024 J. Math. Biol. 89 49
[22] Huang F, Chen X and Wang L 2018 J. Theor. Biol. 449 60
[23] Shi Z, Wei W, Li B, Li C, Li H and Zheng Z 2022 Chaos 32 063138
[24] Erdos P and Renyi A 1961 Acta Math. Hung. 12 261
[25] Newman M E J and Watts D J 1999 Phys. Rev. E 60 7332
[26] Barabasi A L and Albert R 1999 Science 286 509
[27] Lee H W, Cleveland C and Szolnoki A 2022 Appl. Math. Comput. 417 126797
[28] Bahbouhi J E, Bouderba S I, Elkouay A and Moussa N 2024 Appl. Math. Comput. 469 128553
[29] Su L, Yang Z, Zhou B, Zhang N and Li Y 2023 Appl. Math. Comput. 454 128029
[30] Ding R, Wang X, Quan J, Ma S and Zhao J 2025 Chaos, Solitons and Fractals 195 116295
[31] Li Y, Sun H, Han W and Xiong W 2020 Phys. Rev. E 101 042303
[32] Wang J, Dai W, Zheng Y, Yu F, Chen W and Xu W 2024 Chaos, Solitons and Fractals 184 114991 |
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