Research On Evolutionary Game And Its Application According To Finite Resource Competition

At present,the payoff in the literature of two-person symmetric evolution game is almost constant,and there is a big deviation between the model established by constant payoff and some actual phenomena.The paper makes an extended research on the two-person symmetrical evolutionary game on the basis of classical evolutionary game theory starting with the payoff matrix and strategy.The main research work is as follows:(1)The two-person symmetric game with dynamic payoff matrix in competitive environment is studied,and the monotone derivable hypothesis about payoff function is put forward.on this basis,a series of criteria to determine that the equilibrium point is evolutionarily stable strategy are obtained,the detailed proof is given,and verified by specific examples.Because the choice of traffic travel mode is also a symmetrical game in a competitive environment,the payoff of players will decrease or not increase with the increase of the number of people holding the same choice,which has the characteristics of dynamic change,and is consistent with the aforementioned hypothesis.The relevant conclusions of the two-person symmetrical game with dynamic payoff matrix are applied to the study of traffic travel mode selection,which explains that the traffic participants have compared travel mode for a period of time to choose beneficial way is a process of constantly learning and strategy adjusting.In this process,the selection ratio tends to evolutionary stability strategy,which provides guidance for the actual choice of travel tools.(2)The two-person symmetric game under three strategies is studied,the concepts of strategy dimensionality reduction subgame,local subgame,parent game and evolutionary stability strategy are dimension upgrading,and the symmetrical game under three strategies is transformed into two-strategy symmetrical game.The relationship between the evolutionary stability strategy of the two-strategy local sub-game and the evolutionary stability strategy of the three-strategy parent game is studied.Through the study,some criteria about the equilibrium point and the evolutionary stability strategy of the parent game or the evolutionary stability strategy are obtained and illustrated by some examples.Finally,the conclusion of evolutionary stability strategy of three-strategy symmetric game is applied to the choice of traffic travel mode,and it is clarified that under certain conditions,the relative selection ratio of bus and private car when the two-strategy symmetric game is evolutionarily stable is equal to the relative selection ratio of bus and private car when the evolutionary stability is reached in the three-strategy symmetric game.Or the relative selection ratio of subway and bus when the two-strategy symmetric game is evolutionarily stable is equal to the relative selection ratio of subway and bus when it is evolutionarily stable in the three-strategy symmetric game.(3)The application of evolutionary game in mobile location is given.The base station is regarded as a player in the game,a generalized replication dynamic model is constructed,and the algorithm based on three-dimensional space is studied to solve the replication dynamic model.The position of the mobile end is obtained by iterative calculation.When the position distribution of the base station in the three-dimensional space is uneven,especially when the distribution range of the base station in one direction is much larger than the compensation range in another direction,the error of the above iterative algorithm can not be ignored.In order to overcome this defect,the virtual base station is introduced in this paper to reduce the calculation error caused by the large distribution gap.The actual calculation results verify the positive role of the virtual base station in reducing the error.