Game Models And Simulation Research In Some Uncertain Environments

Uncertainty exists widely in our daily lives,and most of us have adapted to making choices in an environment of uncertainty.And Heisenberg's uncertainty principle reveals that the position of a microscopic moving particle and its momentum cannot be determined at the same time,indicating that randomness and contingency are not caused by people's insufficient cognition.Uncertainty is an essential attribute of the world.Usually uncertainty can be divided into random uncertainty and cognitive uncertainty.The mixed strategy in classic games is based on probability theory to express this random uncertainty.And the connotation of uncertainty is so rich,it is not enough to describe uncertainty by probability alone.Game participants often participate in decision-making in an uncertain environment.This uncertainty can be reflected in:participants often cannot truly understand the objective benefits,cannot understand the opponent's strategy,cognitive biases that occur during the game,and Uncertainties generated by self-methods in the cognitive process;therefore,based on game theory,this article incorporates uncertainty into the analysis framework,and studies the application of game theory in modeling and simulation in uncertain environments.The main research results of this paper include the following aspects:(1)Considering that participants often cannot really understand the objective benefits,from a semantic point of view,the Dempster-Shafer evidence theory is used to represent and model uncertain information,and a kind of uncertainty matrix in the semantic environment is studied.Game.And by defining the relative utility relationship of each element in the identification framework,the reliability structure payment matrix is transformed into an equivalent interval number payment matrix,and the interval number is used to describe this income uncertainty.The interval number game method is used to obtain the Nash equilibrium level of each strategy combination,and the Nash equilibrium level is used to replace the definition of Nash equilibrium in the classic game,which provides participants in an uncertain environment to analyze game equilibrium problems and strategy selection problems.New methods and ideas.(2)The uncertainty matrix game is simulated and verified,and the explanation of the mixed strategy in the group is adopted,that is,each strategy in the mixed strategy is reflected in the proportion of individuals who adopt different strategies in the group according to a certain probability.In the simulation experiment,the income of different individuals in the group is set to be different under the same situation,so as to form a income interval in the sense of the group.In this way,it verifies the validity of the uncertainty reliability structure matrix game.(3)Taking into account the widespread existence of uncertainty in the cognitive process,the classic game lacks an endogenous explanation of the game,and does not incorporate cognition and subjective deduction into the analysis.The subjective game theory assumes that the players can learn from the game and summarize them into their own personal views on the game,explaining how the equilibrium of the game is generated from an endogenous point of view.Therefore,based on subjective game theory,discuss the impact of the uncertainty generated in the cognitive process on the outcome of the game.The uncertainty generated in the cognitive process can be uncertainty about whether a certain strategy has been learned,or the deviation between the learned strategy and the actual objective benefit.Introduce the assumption of information disclosure,that is,all the players have learned all the strategies before the start of the game,so as to eliminate the uncertainty generated in the learning process.Compare before and after the information is disclosed,explore the impact of cognitive uncertainty on the outcome of the game.In addition,although the learning model used in subjective games(including reinforcement learning,imitation learning,etc.)reflects a certain degree of uncertainty in the learning process,the content learned is not different from the given game structure,that is to say,what the players think in their hearts is completely consistent with the objective facts.On this basis,this article proposes a new subjective game model.(4)Based on the Eisert-Wilkens-Lewenstein quantum game mechanism,the traditional bank run game model is quantized,and the game model in a random and uncertain environment is studied.The quantum mechanism of EWL under single parameter and double parameter was investigated respectively.The research results show that the quantum bank run game under a single parameter will degenerate into a traditional bank run game;In a two-parameter quantum game,after the quantum entanglement between participants reaches a certain level,the Nash equilibrium with low overall and individual returns will disappear.