广义伪连续下的多主从博弈弱Pareto-Nash均衡的稳定性研究

Study on the Stability of Weak Pareto Nash Equilibrium in Generalized Pseudocontinuous Multi master-slave Games

在现实生活中,许多决策问题都包含多个参与者和多个目标,如企业间的合作博弈、资源共享博弈等。通过探究广义多目标多主从博弈的稳定性,可以制定出更加有效的决策策略和机制,确保参与者能够长期稳定地获得收益并维持合作关系。文章针对Hausdorff拓扑空间内的一种特定的广义多主体-多从体博弈,当其中的参与者支付函数满足广义伪连续性时,研究证明广义多主体-多从体博弈的弱Pareto-Nash均衡解映射存在上半连续性。同时,当参与者支付函数在广义上呈现上伪连续时,也证实了广义多主体-多从体博弈的弱Pareto-Nash均衡解映射的上半连续性。应用本质解的定义,可揭示广义多主体-多从体博弈下弱Pareto-Nash均衡解的稳定性。

In real life,many decision-making processes involve multiple participants and objectives,such as cooperative games between enterprises and resource sharing games.By exploring the stability of generalized multiobjective multi-master-slave games,more effective decision-making strategies and mechanisms can be formulated to safeguard participants'long-term stable returns and maintain cooperative relationships.Taking the example of a specific generalized multi-master-slave game in the Hausdorff topological space,when the participant payment function therein satisfies generalized pseudo-continuity,the study proves that the weak Pareto Nash equilibrium solution mapping exhibits upper semi-continuity.The definition of essential solution can reveal the stability of weak Pareto Nash equilibrium solutions under generalized multi-master-slave game.