Game Theory-based Influence Diagrams With Interval-valued Parameters

With the development of society and technology,people are making many decisions in their lives.The decision-making environment becomes more and more complicated,and contains many uncertain factors,which brings difficulties to the decision-making problem.Influences diagrams(IDs)[1]represent the relationships between the decisions,uncertainties and preferences of decision makers which can be used to evaluate and reveal the optimal strategy and decision makers' value for a decision situation.At present,IDs have become one of the most commonly graphical decision models used for reasoning under uncertainty,and have been widely used in various applications,such as computer science,risk analysis,and artificial intelligence etc.However,this traditional framework still has shortcomings.On the one hand,in some complicated circumstances,especially in interactive decision situations,it is not reasonable to represent the probabilities by sharp-valued and a decision maker can hardly get other decision makers' sharp-valued preference under uncertainty;On the other hand,many decisions are made in interactive situations in which decision makers interact and may also affect each other's decision outcomes in reality.Researchers propose the interval-valued IDs(IIDs)to solve the limit of sharp-value and propose the Game theory-based IDs(GIDs)to make it available in interactive decision situations.In fact,in the process of decision analysis,the more decision makers involved in decision-making,the mutual influence between decision makers and the increase in uncertainty caused by the increase in decision makers,making the sharp-valued parameters of the corresponding nodes become difficult,in order to solve these two problems at the same time,In this paper,we propose a game interval-valued influence diagram(GIID)which extend by IIDs and GIDs.This paper firstly introduces the basic concepts of traditional influence diagrams and game interval-valued influence diagram.Secondly,according to the uncertainty of the interaction problem,a model of game interval-valued influence diagram is established,then propose a method for evaluating GIIDs utilities by decomposing game IDs into non-game IDs.The decomposition is carried out based on Nash equilibrium,such that the actions taken by each decision maker are the best response to the actions taken by the rest of the decision makers.Thirdly,we use the solution of game interval-valued influence diagram with genetic algorithm.Fourthly,The experiments evaluate proposed algorithm in terms of correctness,convergence and efficiency.The results show that our method can effectively solving GIIDs problem.Finally,it is the summary of our work and prospect for the future work.