具有下层目标的多组线性二次微分对策[JZ]的非劣Nash开环策略

引进多组线性二次微分对策的非劣Nash策略的概念,证明非劣Nash策略存在的充分必要条件。在组与组之间Nash竞争而组内部合作的前提下考虑组内第二对策目标,以组内合作权向量为变量构造组与组之间的静态对策问题,得到使第二对策目标平衡的最优合作权向量,进一步得到同时满足第一目标非劣,第二目标平衡的非劣Nash开环策略。最后,以两组经济对策为算例说明该策略的有效性。

Open - Loop Non - inferior Nash Strategies of Linear Quadratic

The conceptions called non-inferior Nash strategies for linear quadratic multi-team differential games are introduced.The necessary and sufficient conditions for its existence are derived.The second objective within each team is investigated in the preconditions of Nash competition between the teams and of cooperation within each team.A static game between the teams for their cooperative weight vectors within each team is established,and the optimal weight vectors of satisfying the equilibrium for the second objectives between the teams are obtained.The open-loop non-inferior Nash strategies of satisfying the non-inferior optimum for the first objective and the equilibrium between the teams for the second objective are developed.Finally,an economic game example in two team systems is presented to illustrate the effectiveness of the strategy.