| 英文摘要 |
Game theory is an important theoretical tool for studying conflict and cooperation issues, widely used in economics, sociology, computer science, military theory, biology and other fields of research. If we explain or predict the real game problems accurately, establishing an appropriate game model is an important prerequisite, and then consider whether the game model has Nash equilibrium and how to find Nash equilibrium. Nash equilibrium is not necessarily unique, even infinite, how to choose a satisfied Nash equilibrium? what are the relationships between Nash equilibriums in the same game model? The main research contents of this thesis are as follows: Firstly, considering the impact of environmental factors, emotions, etc. The players in the game are perturbed when choosing the strategy. By the tools such as set value mapping, fixed point theorem, Ky Fan variational inequality and so on, conservative game model, risk game model and balanced game model are established respectively, then obtain some existence theorems and and some results of stability of Nash equilibrium in these models. Two models are used to analyze how to realize the refinement of Nash equilibriums and the meaning of the model. It is easier to explain the game problems by the equilibriums of the game models which are based on the uncertainty of strategy selection, when the people in the game models are transformed from the complete "rational person" to the "social man". Secondly, the Nash equilibrium of noncooperative game is mainly determined by the best reply mappings of the players in the bimatrix game, therefore, using the best reply mappings of game theory to study the structure of noncooperative game will greatly simplify the complexity brought by the change of payment functions. We try to use the best reply mapping to study the structure of noncooperative game. The relationship between two bimatrix game and transformation on natural number set is established. From the meaning of Baire classification and Lebesgue measure, it is proved that the double matrix games which satisfies (BG) condition are most of the bimatrix games, and all the bimatrix game models satisfying the (BG) condition can be repeated to eliminate the bad strategy and transform it into a game model with the payment matrix as a matrix. By classifying the best reply mappings of the players in the bimatrix game, give the result that the most of the bimatrix games are construct with the two subgames "Game of Battle of Sex" and "Game of Rock-paper-scissors", and study the relations of the Nash equilibrium between the pure strategy and mixed strategy. In the last, establish three hybrid algorithms for solving Nash equilibrium of n-person non-cooperative games. In Dividing algorithm Ⅰ, divid the strategys sets into finite subsets, eliminate the subsets which do not contain Nash equilibiums, by Particle swarm optimization algorithm search Nash equilibriums the subsets which perhaps contain Nash equilibrium. In Dividing Algorithm Ⅱ, divid the strategys sets into finite subsets, and design selection rules and indicate rules of the subsets, then by Fireworks algorithm search Nash equilibriums in the selected subset. In the end, design hybrid algorihms by Particle swarm optimization algorithm and quasi Steepest descent algorithm search Nash equilibriums of the game models with many players or many strategys. Key words: Game theory; Uncertainty; Nash equilibrium; Hybrid intelligent algorithms; Classification.
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