The Improvement Of The Dynamic Quantum Decision Model Of The Prisoner's Dilemma Game

During the recent decade,quantum decision-making models were established based on the mathematical structure and methodologies of quantum mechanics.Owing to the unique theoretical structure,the quantum decision-making models can be applied to explain problems that violate the classical decision models,especially for judgments under uncertainty and decisions under conflicts.Among them,one kind of model called dynamical quantum decision making model which originally derived from Markov decision making models,can be used to explain the disjunction effect and interference effect in decision making.However,there are still some defects in models when the previous models are used to explain the decision making behavior in Prisoner,s delimma Game.Hence,it is of good theoretical and practical significance for the development of dynamical quantum decision model to analysis and overcome these defects.Firstly,the the deficiencies of the previous models were analyzed.We concluded three deficiencies:l)there exists a deviation between previous nodels and their original theoretical construction;2)dynamic nature of the previous models remains doubtful;3)the decision probilities from previous model appeare periodic fluctuations instead of convergence with subjective decision time.In order to overcome these deficiencies,a total of three studies were carried out in this paper.Study 1:Aming at the first deficiency,a model called Full-elements Hamiltonian dynamical quantum model(FH dynamical model)was established to modify this deficiency and a comparison of performance was made between FH dynamical model and previous models study 1.Results showe that FH dynamical model exhibits better fitting and generalization performance.Study 2:Regarding to the last two deficiencies,the dynamical relationship between decision tendency in Prisoner's delimma Game and subjective decision time(time pressure)was investigated in an experiment and attempts were made to fit experimental data by quantum models(including FH dynamical model).Results showe that 1)the probabilities of chosing compete in three different conditions increase along with the increasement of subjective decision time;2)quantum models are not able to fit this dynamical relationship well.Study 3:In order to solve this problem,inspired by dual processing decision making theory,the dual processing dynamical decision model which combines quantum decision making model and Markov decision making model together was established to fit the dynamical decision process in experiment.Results show that the dual processing dynamical decision model not only exhibts lower fitting error but also indicates a better description of the dynamical decision process in experiment.Acombination of three studies can lead to the finding that with better fitting,dynamical and convergence capability,dual processing dynamical decision-making model is a more realistical dynamical decision making model.From the results of this paper,it can be concluded that by combining computational or mathematical quantum model with verbal-conceptual dual processing decision making theory organically,not only the performance of the model can be improved but also a qualitative and quantitative explanation can be achieved.Hence,this ideal model integration deserves much attention and has good theoretical significance and application prospects.