具有模糊支付的Moran过程演化博弈动态

doi:10.12005/orms.2021.0216

运筹与管理 ›› 2021, Vol. 30 ›› Issue (7): 71-76.DOI: 10.12005/orms.2021.0216

具有模糊支付的Moran过程演化博弈动态

王先甲¹, 顾翠伶², 赵金华¹, 全吉³

1.武汉大学经济与管理学院,湖北武汉 430072;
2.河南工业大学管理学院,河南郑州 450001;
3.武汉理工大学管理学院,湖北武汉 430072

收稿日期:2019-03-30 出版日期:2021-07-25
通讯作者: 顾翠伶,女,讲师,研究方向:演化博弈与模糊数学。
作者简介:王先甲(1957-),男,教授,博士生导师,研究方向:博弈论与决策分析;赵金华,男,博士后,研究方向:演化博弈与组合优化;全吉,男,教授,博士生导师,研究方向:演化博弈与复杂系统仿真。
基金资助:
河南工业大学高层次人才基金资助项目(2020BS032);国家自然科学基金资助项目(72031009,71871171,71801175);国家社科基金重大项目(20&ZD058)

Evolutionary Game Dynamics of Moran Process with Fuzzy Payoffs

WANG Xian-jia¹, GU Cuil-ing², ZHAO Jin-hua¹, QUAN Ji³

1. School of Economics and Management, Wuhan University, Wuhan 430072, China;
2. School of Management, Henan University of Technology, Zhengzhou 450001, China;
3. School of Management, Wuhan University of Technology, Wuhan 430072, China

Received:2019-03-30 Online:2021-07-25

摘要/Abstract

摘要： 以往对演化博弈的研究都假设个体从博弈中获得的支付是确定的并以精确的数来表示。然而由于受环境中各种不确定因素的影响,个体博弈时所获得的支付并不是一个精确的数值,而需要用一个模糊数来表示。本文研究模糊支付下2×2的对称博弈, 利用模糊数的运算, 分析具有模糊支付的有限种群Moran过程演化动态。在弱选择下以梯形模糊数和三角模糊数表示博弈支付,计算策略的模糊扎根概率,分析自然选择有利于策略扎根及策略成为模糊演化稳定策略的条件。将经典博弈推广到模糊环境中丰富了演化博弈理论,更具有现实意义。

关键词: 模糊演化博弈, 模糊Moran过程, 模糊数, 模糊扎根概率

Abstract: Previous studies on evolutionary game dynamics have assumed that individuals’ rewards from the game are expressed in exact numbers. However, because of the influence of the various factors from the environment, the payoff obtained by individuals’ interaction is not an exact number. The payoff can be represented by fuzzy numbers. We study 2×2 symmetric games in which the game matrix is represented by fuzzy numbers. The fuzzy fixation probability of the strategy based on fuzzy game matrix is calculated by using the operation relation of fuzzy numbers. In the form of triangular fuzzy number and trapezoid fuzzy number, numerical analysis is carried out. Numerical examples demonstrate the feasibility and validity of the new method. We obtain the conditions that natural selection is favorable for a strategy to take fixation and a strategy to be a FESS. It is more realistic to promote the classical game to the fuzzy environment and also enrich the theory of evolutionary game.

Key words: fuzzy evolutionary game, fuzzy Moran process, fuzzy numbers, fuzzy fixation probability

中图分类号:

O159
F224

王先甲, 顾翠伶, 赵金华, 全吉. 具有模糊支付的Moran过程演化博弈动态[J]. 运筹与管理, 2021, 30(7): 71-76.

WANG Xian-jia, GU Cuil-ing, ZHAO Jin-hua, QUAN Ji. Evolutionary Game Dynamics of Moran Process with Fuzzy Payoffs[J]. Operations Research and Management Science, 2021, 30(7): 71-76.

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具有模糊支付的Moran过程演化博弈动态

Evolutionary Game Dynamics of Moran Process with Fuzzy Payoffs

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