社会均衡存在定理与Nash均衡存在定理及其关系

文章引入带约束条件的博弈概念,说明相应的博弈和它的扩充博弈的Nash均衡在带约束条件博弈下具有一致性,指出N ash均衡存在定理I和II的证明方法是雷同的;叙述并证明社会均衡存在定理.利用社会均衡存在定理给出Nash均衡存在定理I、II和III的另一种证明,从而也就说明了这三个N ash均衡存在性定理证明之间的关系,其中还给出纳什均衡存在定理III的一种证明以及给出它的一个推论.

The Social and Nash Equilibrium Existence Theorems and the Relation of the Theorems

The paper introduces the concept of game with constraint condition,and illustrates the consistency of the corresponding and their extended games under games with constraint condition,and indicates that methods of proving Nash equilibrium existence theorem I and II are similar,and presents and proves the social equilibrium and its existence theorem.Using the social equilibrium existence theorem it gives other proof of Nash equilibrium existence theorem I,II and III,and thus explains the relation to proofs of three theorems,and there it provides also one proof of Nash equilibrium existence theorem III and its a corollary.