群体博弈合作均衡的存在性和适定性研究

针对许多经济问题面临着大规模大群体之间的策略互动, 且策略互动时,参与主体之间为寻求更高利益可 能达成合作的行为, 研究群体博弈合作均衡的存在性,为这些情况提供统一分析框架。 首先, 介绍群体博弈模型 及群体博弈合作均衡的定义;其次,在群体状态函数为伪连续的条件下, 构造辅助偏好映射, 借助伪连续的性质, 得到群体博弈问题合作均衡的存在性结果, 并举例说明该存在性定理的优越性。 针对求解群体博弈合作均衡时, 原始数据收集可能会出现偏差, 模型数据可能受到干扰, 求解的近似解序列可能不可行的情形, 研究群体博弈合 作均衡的适定性,为数值计算提供理论依据。 首先, 分别引入该类群体博弈问题合作均衡的 Hadamard 适定性和 Levitin-Polyak 适定性概念;然后, 借助合作均衡映射的半连续性和紧性结果, 建立 Hadamard 适定性成立的充分性 条件;最后, 借助群体状态函数的伪连续性, 建立 Levitin-Polyak 适定性成立的充分性条件。

The Existence and Well-posedness of Cooperative Equilibrium for Population Games

For many economic problems facing large-scale strategic interactions between large groups and when strategic interactions occur participants may cooperate to seek higher benefits. Studying the existence of cooperative equilibrium in population games provides a unified analytical framework for these situations. In this paper we first introduced the model of population games and the definition of cooperative equilibrium in these games. Secondly under the condition that the population state function was pseudo continuous an auxiliary preference mapping was constructed. With the aid of the property of pseudo continuity an existence theorem for cooperative equilibrium of population games was established and an example was given to illustrate its advantages. When solving cooperative equilibrium in population games there may be deviations in the collection of original data model data may be disturbed and the approximate solution sequence may not be feasible. Studying the well-posedness of cooperative equilibriums of population games provides a theoretical basis for numerical calculation. The concepts of Hadamard well-posedness and Levitin Polyak well-posedness of cooperative equilibrium of population games were introduced. By the semicontinuity and compactness of cooperative equilibrium mappings sufficient conditions of Hadamard well-posedness were established. At last by the pseudo-continuity of the population state function sufficient conditions of Levitin-Polyak well-posedness were established.