【作者】 顾建庄；

【导师】 宋振明；

【作者基本信息】 西南交通大学 ， 应用数学， 2004， 硕士

【摘要】 在现实世界中的许多决策问题中，决策者所考虑的目标往往不只一个，而是通过综合多个主要目标进行决策，多目标决策比单目标决策更符合客观实际，可以提高决策的科学性。多目标博弈是解决现实社会中具有多个目标的多个决策主体之间相互作用等众多错综复杂问题的有效分析方法，因此，研究多目标博弈具有重要的现实意义。 关于多目标博弈，已经相继出现了一些研究成果：多目标博弈解的概念，多目标定性微分博弈，约束多目标博弈，多目标Nash协商博弈，模糊多目标博弈等。 首先本文介绍了目前解决多目标博弈问题的主要方法：Pareto向量最优法，权系数法，权系数联合模糊多目标法和最小分量联合模糊多目标法等。但是对于决策者在要求达到这些目标时，有主次或轻重缓急的不同，也就是说，多个目标分优先等级(层次)的情况，至今还没有讨论。 接着本文把目标规划的思想运用到多目标博弈中，通过运用Nash均衡原理，给出了新的多目标博弈均衡解概念：强满意均衡解集和弱满意均衡解集。在实例分析中，运用本文所得到的方法，对改进的Bertrand双寡头博弈模型进行了讨论，解释了现实生活中关于价格战的跟进与不跟进现象。 最后本文还提出了一种涵盖权系数法的多目标博弈处理方法：西南交通大学硕士研究生学位论文第日页基于模糊综合评判的联合多目标博弈方法，此方法是对权系数法的一种扩展。更多还原

【Abstract】 Deciders usually have not only one objective to consider. Deciders integrate many objectives in decision-making. Multi-objective decision is more consistent with realism than single objective decision and can make decisions precise. Multi-objective game is an effective method to solve reciprocity between many deciders. So, it is important to study multi-objective games.As a branch of game theory, multi-objective game theory has attracted quite a few scholars’ interest. A few research achievements appeared and mainly introduced: the concept of equilibrium solution of multi-objective games, qualitative differential games with multiple objectives, multi-objective games with restricted condition, multi-objective Nash bargaining games, fuzzy multi-objective games and so on.Firstly, this paper introduces the most used methods of solving multi-objective games: the method of Pareto vector superior, weighting coefficients, weighting coefficients aggregated multiple objectives and minimum component aggregated multiple objectives. But to this day, some games with multiple objectives which are different in importance or emergency, namely objectives have their own orders are not discussed.Secondly, this paper uses the thought to multi-objective games and gives the concepts of strong satisfied equilibrium solution set and feeble satisfied equilibrium solution set by using Nash equilibrium theory. A concrete case improved Bertrand double oligarchs model is discussed by using the methods of this paper in the example, and successfully explains the phenomena of following and no following in price war.At last, this paper also puts forward a new method to solve multi-objective games: aggregated multi-objective games based on fuzzy comprehensive evaluation. This method overcasts the method of weighting coefficients and extends of weighting coefficients.更多还原