A Third-Party Punishment Function Model On Fairness Preference

Abstract:The traditional assumption of "rationality" is widely suspected by other economic branches increasingly.Much phenomenon breaches the economic exception of traditional theory in the real life.Through all kinds of experiments,behavioral economics and experimental economics prove that our decisions rely not only on the absolute benefit,but it is also influenced by various psychological factors,such as fairness,intention,cooperation,social welfare.Among all the factors,fairness preference is a significant impact factor.In our daily life,we can see some phenomenon about fighting with crimes and behaving righteously.When we see the benefit loss of others,we will punish the one who takes advantage although it is none of our business.Recently,we can also see the fighting with crimes and behaving righteously,news and reports about these are common occurrence as well.Scholars modeled variously to discuss how mental factors affect human utility and then human behaving and decision.Among those,Robin's model is regarded as the first utility model based on fairness preference.Later,all kinds of model functions were found by scholars,which contain intention,kindness,reciprocal,social welfare and so on.In this way they try to explain human behaving by solving the individual utility maximization problems.The main form of utility function scholars used before is x plus f.x is individual profit and f is quantization of mental factors scholars put in the model,which affect human utility.For f,there are two main common forms.One is utility loss stemmed from profit difference,including subjective intention,result difference.The other is social total welfare.Scholars think people care about not only self-profit,but they also concern social total welfare.But these two have obvious disadvantage.As x is first order form and it directly plus the mental factors part,we can't analyze the interaction between both.Particularly,we can't solve this utility maximization problem by using first order condition.For there is no model about third-party punishment.This paper,based on the traditional fairness preference model,propose a new model which consider the fairness aversion of benefit between other two people.We use it to analyze the third-party punishment dictator game by linear and logarithmic function.Also,we explain the behaving and influence factor of third-party punishment and provide some suggestions and prospect according to the conclusion of this model.