Study On Decision Tree Model Based On Non-expected Utility Theory And Its Application

Since the beginning of the world,expected utility theory has been favored by mainstream economists and management scientists.Expected utility theory has been applied to the theoretical basic research of uncertain decision-making activities.However,in recent decades,with the development of behavioral science and the rise of experimental economics and gradually integrated into the mainstream research,there have been a large number of empirical evidence contradicting the expected utility theory.Therefore,the expected utility theory,as the theoretical basis of uncertain decision-making activities,has been widely questioned by the majority of economists and management scientists.In the process of trying to find an alternative theory of expected utility theory,various disciplines have produced a variety of non-expected utility theories.Among them,the scope-dependent utility theory is the outstanding representative.Although due to the limitations of expected utility theory in practical decision-making,there are many paradoxes,such as common ratio effect,common consequence effect,the coexistence of insurance and gambling,which cause people to replace or weaken most of the rational preference conditions.however,the rational requirement of first-order random dominance has always been unwilling to give up.Before the emergence of range-dependent utility theory,it was generally believed that in order to explain these paradoxes,it was necessary to introduce a certain probability weight(the evaluation function has nonlinear probability).The scope-dependent utility model can explain these paradoxes without probability weighting,which is the advantage of scope-dependent utility theory over nonlinear probabilistic non-expected utility theory.because it is easier to meet the rational requirement of first-order random dominance.When solving problems related to compound prospects,it is often necessary to simplify them to simple prospects,which will provide the necessary simplicity for problem solving.The compound independent axiom put forward by Segal is different from the traditional compound prospect simplification axiom.It does not change the basic structure of the compound prospect and will not cause many anomalies.It is a more objective and practical simplificationmethod.Based on the theory of scope-dependent utility and the compound axiom of independence,this paper constructs a decision tree model based on scope-dependent utility.The basic idea of the model is that when analyzing the bottom prospect of the decision tree,the evaluation value of the prospect is obtained by using the decision utility function in the range dependent utility model.Because of the existence of the compound independent axiom,all the bottom foreground evaluation values can be taken as the results of the upper foreground,so the upper composite prospect is simplified to another simple prospect,and the decision utility function in the scope dependent utility model is used again to obtain the evaluation value of the upper foreground.According to this idea,the evaluation value of each scheme corresponding to the decision branch of the decision tree can be obtained by recursive from the low end of the decision tree,and the decision maker can choose the scheme with the greatest evaluation value by selecting the best.In the fourth chapter,in the application of the model case,the model is applied to the actual decision case by using the above basic ideas,the optimal choice of the decision scheme is obtained,and the improvement of the model to the traditional decision tree model based on expected utility theory is analyzed and expounded.As mentioned above,this model has a high application value,but also has a certain theoretical value,the introduction of non-expected utility theory into the decision tree model,more in line with the actual decision-making process.