互惠利他行为的演化模型与仿真
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摘要
利他行为无论在生物种群的演化过程还是在人类社会的发展中,无论是在历史还是在现实生活中,都是普遍存在的,它是维持人类繁衍并保持社会稳定的重要因素。福利经济学中的很多问题可以用利他行为来解释。利他行为不仅是心理学、社会学、哲学等学科关心的问题,也是经济学、管理学所研究的课题。
利他行为是典型的有限理性行为,本文研究利他行为的演化规律和生存条件,分析利他与利己在演化中的共生关系,这对研究行为经济学与行为科学、对研究和谐社会的构建机制都具有积极意义。
本文采用了经济学家在研究生态种群演化中的观点,将人群在演化博弈中的收益定义为人群的适应度,即人群的繁殖率或数量上的增长;将人的行为的演化,转化为行为者为适应环境而发生的人数的变化。由于人的行为受到所面临的问题和环境的影响,假定行为者面临的问题是确定的,行为仅受周围人群的影响随时间而变化,行为者的人数可测量。为了能借助连续模型来研究相关问题,进一步假定行为者的人数是时间的连续可微函数。
本文的主要工作是:
构造了有限理性下效用函数及利他系数的数学表达式;将有限理性下的个人效用函数代替完全理性假设下的个人收益,研究了一类博弈在有限理性下的和谐解。
构建了利他行为的演化模型,证明了当收益与支付相比足够大时,利他行为能够存在。仿真验证了利他行为者的理性羊群行为的收敛性。
引进利他行为系数,建立了利他行为的重复博弈模型,证明了利他行为在一定条件下在重复博弈中能够生存。构建了利他行为的最优反应动态和虚拟行动的学习模型,在两种模型中证明了互惠形式的利他行为在一定条件下收敛到均衡。将利他系数作为系统演化过程中的内生变量,研究了利他系数随着学习博弈的演化而趋于稳定的规律。
研究了利他行为者与利己行为者在竞争共生模型中的演化规律,分别建立了在生存条件无限制与有限制、利己行为者能够单独生存与不能单独生存的两类人相互作用的系统模型。通过稳定性分析和仿真发现:在利他行为者利他能力很强或者利己行为者利己能力较弱的情况下,社会系统是稳定;由单一人群组成的社会是不稳定的;在没有生存条件限制或环境最大承载能力随人群数量而增大时,社会系统是周期性变化或者具有结构稳定性(对应的微分方程存在周期解或极限环)。
本文的模型与结论有益于研究经济行为的规律,有益于研究合作机制的形成。
The altruistic behavior exists widely in the evolutionary process of the population of the animal and humanity. It is an important factor in the population growth and keeping the stability of the society. We are interested in that many problems in the welfare economics can be explained with the altruistic behavior which is well studied in psychology, sociology, philosophy, administration and economics.
Altruistic behavior is a kind of typical behavior of limited rationality. The evolutionary rule and the survival conditions of the altruistic behavior have been studied, and the competition and coexistence in the evolutionary process of the reciprocal altruist and selfish behavior has been analyzed. It is meaningful for the study of Behavioral Economics and Behavior Science, and for the building of the mechanism of the harmonious society.
The payoff in the evolutionary games is defined as fitness (the increasing rate of population) of the population with the opinion of the economist in the studying to the population evolution. The evolution of the population behavior has been looked upon as the change of the subject's number in the process for suiting the environment. As the subject's behavior changes along with the different problems and environment, the problem is fixed in the games, the behavior is influenced by the environment only, the subject's number is a measurable, continuous and differentiable function of time in the continuous models.
The main creative results are as following:
The mathematical expressions of the utility function and althuistic coefficient with limited rationality are structuralized and the harmonious solution is studied in a kind of gemes replacing the payoff in tranditional games with the utility function of limited rationality.
The evolutionary model for altruistic behavior is set up based on the S.& W. model.. A sufficient and necessary condition for the survival of altruistic behavior is given. The evolutionary simulation of the altruistic herd behavior verifies the convergence.
The infinitely repeated game for altruistic behavior is instructed with altruistic behavior coeffient and the conclusion is proved that the social efficacy with a punishment mechanism can be achieved. And the equilibriums of the evolutionary dynamics of the altruistic behavior and selfish behavior are proved in the Fictitious Play and Best Response Dynamics.. The althuisitc coefficient as an endogenous parameter is convergent with the convergence of the evolutionary games.
The competition and coexistence models of altruistic and selfish are built under some hypothesis for existing environment: if the environment has capacity restriction or not; if the selfish agent can survive alone or not. Some results are studied using the stability analysis and simulation that the society is stable if the altruistic capacity of the altruistic is stronger or the selfish capacity of the selfish is weaker, the society consisted by a single kind of population isn't stable and the society system is periodic or structural stable when it hasn't the survival restriction or the bearing capacity of the environment is growing as the population increasing.
The models and conclusions are helpful to analyze the economic behavior and the mechanism of the harmony.
利他行为是典型的有限理性行为,本文研究利他行为的演化规律和生存条件,分析利他与利己在演化中的共生关系,这对研究行为经济学与行为科学、对研究和谐社会的构建机制都具有积极意义。
本文采用了经济学家在研究生态种群演化中的观点,将人群在演化博弈中的收益定义为人群的适应度,即人群的繁殖率或数量上的增长;将人的行为的演化,转化为行为者为适应环境而发生的人数的变化。由于人的行为受到所面临的问题和环境的影响,假定行为者面临的问题是确定的,行为仅受周围人群的影响随时间而变化,行为者的人数可测量。为了能借助连续模型来研究相关问题,进一步假定行为者的人数是时间的连续可微函数。
本文的主要工作是:
构造了有限理性下效用函数及利他系数的数学表达式;将有限理性下的个人效用函数代替完全理性假设下的个人收益,研究了一类博弈在有限理性下的和谐解。
构建了利他行为的演化模型,证明了当收益与支付相比足够大时,利他行为能够存在。仿真验证了利他行为者的理性羊群行为的收敛性。
引进利他行为系数,建立了利他行为的重复博弈模型,证明了利他行为在一定条件下在重复博弈中能够生存。构建了利他行为的最优反应动态和虚拟行动的学习模型,在两种模型中证明了互惠形式的利他行为在一定条件下收敛到均衡。将利他系数作为系统演化过程中的内生变量,研究了利他系数随着学习博弈的演化而趋于稳定的规律。
研究了利他行为者与利己行为者在竞争共生模型中的演化规律,分别建立了在生存条件无限制与有限制、利己行为者能够单独生存与不能单独生存的两类人相互作用的系统模型。通过稳定性分析和仿真发现:在利他行为者利他能力很强或者利己行为者利己能力较弱的情况下,社会系统是稳定;由单一人群组成的社会是不稳定的;在没有生存条件限制或环境最大承载能力随人群数量而增大时,社会系统是周期性变化或者具有结构稳定性(对应的微分方程存在周期解或极限环)。
本文的模型与结论有益于研究经济行为的规律,有益于研究合作机制的形成。
The altruistic behavior exists widely in the evolutionary process of the population of the animal and humanity. It is an important factor in the population growth and keeping the stability of the society. We are interested in that many problems in the welfare economics can be explained with the altruistic behavior which is well studied in psychology, sociology, philosophy, administration and economics.
Altruistic behavior is a kind of typical behavior of limited rationality. The evolutionary rule and the survival conditions of the altruistic behavior have been studied, and the competition and coexistence in the evolutionary process of the reciprocal altruist and selfish behavior has been analyzed. It is meaningful for the study of Behavioral Economics and Behavior Science, and for the building of the mechanism of the harmonious society.
The payoff in the evolutionary games is defined as fitness (the increasing rate of population) of the population with the opinion of the economist in the studying to the population evolution. The evolution of the population behavior has been looked upon as the change of the subject's number in the process for suiting the environment. As the subject's behavior changes along with the different problems and environment, the problem is fixed in the games, the behavior is influenced by the environment only, the subject's number is a measurable, continuous and differentiable function of time in the continuous models.
The main creative results are as following:
The mathematical expressions of the utility function and althuistic coefficient with limited rationality are structuralized and the harmonious solution is studied in a kind of gemes replacing the payoff in tranditional games with the utility function of limited rationality.
The evolutionary model for altruistic behavior is set up based on the S.& W. model.. A sufficient and necessary condition for the survival of altruistic behavior is given. The evolutionary simulation of the altruistic herd behavior verifies the convergence.
The infinitely repeated game for altruistic behavior is instructed with altruistic behavior coeffient and the conclusion is proved that the social efficacy with a punishment mechanism can be achieved. And the equilibriums of the evolutionary dynamics of the altruistic behavior and selfish behavior are proved in the Fictitious Play and Best Response Dynamics.. The althuisitc coefficient as an endogenous parameter is convergent with the convergence of the evolutionary games.
The competition and coexistence models of altruistic and selfish are built under some hypothesis for existing environment: if the environment has capacity restriction or not; if the selfish agent can survive alone or not. Some results are studied using the stability analysis and simulation that the society is stable if the altruistic capacity of the altruistic is stronger or the selfish capacity of the selfish is weaker, the society consisted by a single kind of population isn't stable and the society system is periodic or structural stable when it hasn't the survival restriction or the bearing capacity of the environment is growing as the population increasing.
The models and conclusions are helpful to analyze the economic behavior and the mechanism of the harmony.
引文
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