群体博弈理论的新进展

doi:10.15960/j.cnki.issn.1007-6093.2024.03.002

Abstract

Abstract:

Population game theory is a new direction of game theory, developed in recent thirty years, which originated from "Mass-Action" interpretation on mixed strategies and equilibria in 1950 by J. Nash in his PhD dissertation. It established rational decision making theory for individuals in population and society consisting of large number of individuals, and has been applied extensively and intensively in sociology, biology, economics, management science and information science, etc. In this paper, we give a review on recent advances of population game theory and investigate new developing directions.

Key words: population game, Nash equilibrium, cooperative equilibrium, multiobjective population game, Pareto-Nash equilibrium

CLC Number:

O225

Hui YANG. New advances in population game theory[J]. Operations Research Transactions, 2024, 28(3): 27-45.

References 42

1	von Nuemann J , Morgenstern O . Theory of Games and Economic Behavior[M]. Princeton: Prentice-Hall, 1944.
2	Nash J . Equilibrium points in n-person games[J]. Proceedings of the National Academy of Sciences of the United States of America, 1950, 36, 48- 49.
3	Nash J . Noncoopertive games[J]. Annals of Mathematics, 1951, 54, 286- 295. doi: 10.2307/1969529
4	Nash J. N-person nonooprative games[D]. Princeton: Princeton University, 1950.
5	Blume L. Population Games[R]. New Mexico: Santa Fe Institute, 1996.
6	Sandholm W H . Population Games and Evolutionary Dynamics[M]. Cambridge: MIT Press, 2010.
7	Selten R . Reexamination of the perfectness concept for equilibrium points in extensive game[J]. International Journal of Game Theory, 1975, 4, 25- 55. doi: 10.1007/BF01766400
8	Myerson R . Refinements of the Nash equilibrium concept[J]. International Journal of Game Theory, 1978, 7, 73- 80. doi: 10.1007/BF01753236
9	仲崇轶. 群体博弈的有限理性问题及演化动力学研究[D]. 贵阳: 贵州大学, 2020.
10	Wu W T , Jiang J H . Essential equilibrium points of n-person noncoopertive games[J]. Scientia Sinica, 1962, 11, 1307- 1322.
11	Jiang J H . Essential component of the set of fixed points of the multivalued mappings and its application to the theory of games[J]. Scientia Sinica, 1963, 7, 951- 964.
12	Kohlberg E , Mertens J . On the strategic stability of equilibria[J]. Economitrica, 1986, 54, 1003- 1037. doi: 10.2307/1912320
13	俞建. 对策论中的本质平衡[J]. 应用数学学报, 1993, 16, 153- 157.
14	Yu J . Essential equilibria of n-person noncoopertive games[J]. Journal of Mathematical Economics, 1999, 31, 361- 372. doi: 10.1016/S0304-4068(97)00060-8
15	Yu J , Xiang S W . Essential components of equilibria of n-person noncoopertive games[J]. Nonlinear Analysis: TMA, 1999, 38, 259- 264. doi: 10.1016/S0362-546X(98)00193-X
16	俞建. Nash平衡的存在性与稳定性[J]. 系统科学与数学, 2002, 22, 296- 311.
17	Yang H , Yu J . On essential components of the set of weakly Pareto-Nash equilibrium points[J]. Applied Mathematics Letters, 2002, 15, 553- 560. doi: 10.1016/S0893-9659(02)80006-4
18	Yu J , Yang H , Xiang S W . Unified approach to existence and stability of essential components[J]. Nonlinear Analysis: TMA, 2005, 63, e2415- e2425. doi: 10.1016/j.na.2005.03.048
19	俞建. 博弈论与非线性分析[M]. 北京: 科学出版社, 2008.
20	Yang Z , Zhang H Q . Essential stability of cooperative equilibria for population games[J]. Optimization Letters, 2019, 13, 1573- 1582. doi: 10.1007/s11590-018-1303-5
21	张海群. 种群博弈中合作均衡的存在性与稳定性研究[D]. 上海: 上海财经大学, 2020.
22	张海群. 有限理性与一类群体博弈弱有效Nash均衡的稳定性[J]. 数学物理学报, A辑, 2023, 4, 432- 447.
23	Kajii A . A generalization of Scarf's theorem: An α-core existence theorem without transitivity or completeness[J]. Journal of Economic Theory, 1992, 56, 194- 205. doi: 10.1016/0022-0531(92)90076-T
24	张弦. 多主从群体博弈中合作均衡的存在性[J]. 应用数学学报, 2022, 2, 197- 211.
25	武文俊, 杨光惠, 房才雅, 等. 主从群体博弈合作均衡的通有稳定性[J]. 数学物理学报, A辑, 2023, 43, 921- 929.
26	Yang G H , Yang H . Stability of weakly Pareto-Nash equilibria and Pareto-Nash equilibria for multiobjective population games[J]. Set-Valued and Variational Analysis, 2017, 25, 427- 439. doi: 10.1007/s11228-016-0391-6
27	Yang G H , Yang H , Song Q Q . Stability of weighted Nash equilibria for multiobjective population games[J]. Journal of Nonlinear Science and Applications, 2016, 9 (3): 4167- 4176.
28	杨光惠. 多目标群体博弈平衡的精炼[D]. 贵阳: 贵州大学, 2017.
29	赵薇, 杨辉, 吴隽永. 不确定参数下群体博弈均衡的存在性与通有稳定性[J]. 应用数学学报, 2020, 43 (4): 627- 638.
30	王明婷, 杨光惠, 杨辉. 有限理性下不确定性群体博弈弱NS平衡的稳定性[J]. 数学物理学报, A辑, 2022, 6, 1812- 1825.
31	Wang G , Liu Z , Yang H , et al. Existence of equilibrium solutions for multi-objective population games with fuzzy parameters[J]. Fuzzy Sets and Systems, 2023, 473, 108698. doi: 10.1016/j.fss.2023.108698
32	Maynard Smith J , Price R . The logic of animal conflict[J]. Nature, 1973, 246, 15- 18. doi: 10.1038/246015a0
33	Pi J X , Yang G H , Yang H . Evolutionary dynamics of cooperation in N-person snowdrift games with peer punishment and individual disguise[J]. Physica A: Statistical Mechanics and its Applications, 2022, 592, 126839. doi: 10.1016/j.physa.2021.126839
34	Pi J X , Yang G H , Tang W , et al. Stochastically stable equilibria for evolutionary snowdrift games with time costs[J]. Physica A: Statistical Mechanics and Its Applications, 2022, 604, 127927. doi: 10.1016/j.physa.2022.127927
35	Bi Y , Yang H . Based on reputation consistent strategy times promotes cooperation in spatial prisoner's dilemma game[J]. Applied Mathematics and Computation, 2023, 444, 127818. doi: 10.1016/j.amc.2022.127818
36	Bi Y , Yang H . Heterogeneity of strategy persistence promotes cooperation in spatial prisoner's dilemma game[J]. Physica A: Statistical Mechanics and Its Applications, 2023, 624, 128939. doi: 10.1016/j.physa.2023.128939
37	Bi Y , Yang H . Heterogeneous reputation promotes cooperation in spatial public goods game[J]. Physics Letters A, 2023, 488, 129149. doi: 10.1016/j.physleta.2023.129149
38	Zhou D , Pi J X , Yang G H , et al. Nonlinear dynamics of a heterogeneous quantum Commons' tragedy[J]. Physica A: Statistical Mechanics and Its Applications, 2022, 608, 128231. doi: 10.1016/j.physa.2022.128231
39	Zhou D , Yang H , Pi J X , et al. The dynamics of a quantum Cournot duopoly with asymmetric information and heterogeneous players[J]. Physics Letters A, 2023, 192033.
40	Larbani M . Non-cooperative fuzzy games in normal form: A survey[J]. Fuzzy Sets and Systems, 2009, 160 (22): 3184- 3210. doi: 10.1016/j.fss.2009.02.026
41	Liu B D . Uncertainty Theory[M]. New York: Springer, 2010.
42	袁先智. 共识博弈与区块链生态共识均衡[J]. 运筹学学报(中英文), 2024, 28 (3): 1- 26.

[1]	Zhe YANG. Strong Nash equilibria of games with additively coupled utilities and a continuum of players [J]. Operations Research Transactions, 2024, 28(3): 143-152.
[2]	Zhigang CAO, Jin SONG, Sijie WANG, Feng ZHU. Interpretations of the nonexistence of equilibrium in game theory and economics [J]. Operations Research Transactions, 2024, 28(3): 132-142.
[3]	Jian HOU, Mengmeng LI, Zhu WEN. The method for a class of Nash equilibrium game [J]. Operations Research Transactions, 2023, 27(3): 129-136.
[4]	Xinya HE, Ailing GU. Optimal reinsurance investment strategies of two competing insurance companies under VaR constraints [J]. Operations Research Transactions, 2023, 27(3): 1-20.
[5]	Xiayan CHENG, Yin HE, Congcong ZHAO, Rongheng LI. Tight Price of Anarchy for selfish task scheduling on two selfish machines [J]. Operations Research Transactions, 2022, 26(3): 109-119.
[6]	LIN Yang, WANG Yingming. Two-sided game matching with uncertain preference ordinal [J]. Operations Research Transactions, 2020, 24(1): 155-162.
[7]	XUE Juan, GAO Hongwei, JIANG Hui, ZHOU Yunxun. Two-person stochastic game model of data transmission based on slotted ALOHA protocol [J]. Operations Research Transactions, 2019, 23(4): 45-58.
[8]	HOU Lina, SUN Hailin. Two-stage stochastic non-cooperative multi-vendor game under the transportation network-based on stochastic variational inequarity [J]. Operations Research Transactions, 2019, 23(3): 91-108.
[9]	ZHANG Long, ZHANG Yuzhong, BAI Qingguo. Existence of Nash equilibria in scheduling game on limited machines with activation cost [J]. Operations Research Transactions, 2018, 22(1): 87-96.
[10]	WANG Lei, LIN Chong, GU Yan, LIU Cui, GAO Hongwei. Strategic stability of cooperative solutions in infinite stage network games [J]. Operations Research Transactions, 2018, 22(1): 77-86.
[11]	XU Yisong, WANG Yingming. A ranking method for the assignment problem with mutiple optimal solutions [J]. Operations Research Transactions, 2014, 18(2): 96-102.
[12]	Leon A. Petrosyan. Coalitional solutions in differential games [J]. Operations Research Transactions, 2012, 16(4): 86-94.
[13]	Weiqi Liu Yan Ma Jihong Li. Equilibrium balking strategy in the Geo/Geo/1(E,SV) queueing system [J]. Operations Research Transactions, 2012, 16(2): 65-76.

New advances in population game theory

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References 42

Related Articles 13

Recommended Articles

Metrics

Comments