摘要
本文推广了二重最优耦合的概念,得到结果 I:设X和Y是Polish空间,φ:X×Y→R可测,μ∈P(X),ν∈P(Y),(i)如果φ是有下界的下半连续函数,那么φ最优耦合γφ存在;(ii)如果φ是有上界的上半连续函数,那么φ上最优耦合γφ存在.结果 II:设Gi(i=1, 2)是从可测空间(?i, Fi)到Polish空间(Xi,ρi, B(Xi))上的转移概率测度序列,(i)如果φ:X1×X2→R是有下界的下半连续函数,则G1和G2的φ最优可测耦合存在;(ii)如果φ:X1×X2→R是有上界的上半连续函数,则G1和G2的φ上最优可测耦合存在.本文提出一种带约束的n重最优耦合的概念并证明这种最优耦合的存在性,由此定义了一种博弈论中的Nash均衡的最优合作均衡,并举例说明这种新均衡优于Nash均衡.
In this paper, we extend the concept of binary optimal coupling. We obtain the result I: Suppose X and Y are Polish spaces, φ : X × Y → R is measurable, μ ∈ P(X), ν ∈ P(Y).(i) If φ is a lower semi-continuous function with a lower bound, then φ optimal coupling γφ exists;(ii) if φ is an upper semi-continuous function with an upper bound, then φ upper optimal coupling γφ exists. In addition, we obtain the result II: Suppose Gi(i = 1, 2) is a transition probability measure sequence.(i) If φ : X1 × X2 → R is a lower semi-continuous function with a lower bound, then φ optimal coupling of G1 and G2 exist;(ii) if φ : X1 × X2 → R is an upper semicontinuous function with an upper bound, then φ upper optimal coupling G1 and G2 exist. A concept of n-fold optimal coupling with constraints is presented and the existence of this optimal coupling is proved. Furthermore,an optimal cooperation equilibrium of Nash equilibrium in game theory is defined. This equilibrium is superior to Nash equilibrium as illustrated.
作者
张绍义
张韧
Shaoyi Zhang;Ren Zhang
出处
《中国科学：数学》
CSCD
北大核心
2020年第1期197-210,共14页
Scientia Sinica：Mathematica
基金
应用数学湖北省重点实验室资助项目
