本质连通区的存在性和稳定性

本文首先给出了一个统一的本质连通区的存在性定理．应用这个定理，容易地导出了不动点集和Nash平衡点集本质连通区的存在性定理．此外，还首先给出了一个统一的本质连通区的稳定性定理．     

图象拓扑下的Ky Fan引理解集的本质连通区及其在对策论上的应用

本文在集值映射的图象拓扑意义下,证明了赋范线性空间中的Ky Fan引理的解集的本质连通区的存在性,由此得到一类对策的Nash平衡点集的本质连通区的存在性.     

无穷维向量优化问题的本质解及解集的本质连通区

对向量优化引入本质解和解集的本质连通区的概念,研究一般向量优化问题(包括无穷维的)弱有效解集的稳定性.证明了满足一定条件的向量优化问题构成的完备度量空间中,存在一个稠密Gδ集,在此稠密Gδ集中每个问题的解集都是稳定的,推广了文献中的相应结果.进一步讨论了解集的本质连通区,证明了如果解集能分解成两个或两个以上的连通区,则该问题没有本质连通区.最后给出了一个本质连通区存在的充分必要条件.     

锥弱有效解的本质集和本质连通区

对于多目标规划问题,通过引入锥弱有效解集的概念,证明了任何连续有界泛函至少存在一个极小本质集和一个本质连通区.     

关于无限对策Nash平衡点集的本质连通区

证明了任意纯策略集是紧度量空间和支付函数连续的n人无限非合作对策存在 Nash平衡点集的本质连通区．     

拟变分不等式解集的极小本质集及应用

引入了拟变分不等式解集的极小本质集的概念，并证明了每个拟变分不等式(满足一定条件)的解集至少存在一个极小本质集．作为应用，还证明了大多数(在Baire分类意义下)拟-似变分不等式问题的解集是稳定的；每个拟-似变分不等式(满足一定条件)的解集至少存在一个本质连通区．     

信息集广义多目标博弈弱Pareto-Nash平衡点的存在性和稳定性

首先把信息集的概念引入到多目标博弈, 建立了信息集广义多目标博弈模型, 并指出了信息集广义多目标博弈以广义多目标博弈、广义n人非合作博弈、一般n人非合作博弈为特例, 然后用Fan-Glicksberg不动点定理证明了信息集广义多目标博弈弱Pareto-Nash平衡点的存在性, 最后在本质解和强本质解的意义下, 分别研究了信息集广义多目标博弈弱Pareto-Nash平衡点的通有稳定性和强本质连通区的存在性.     

对称集值向量拟均衡问题解集的稳定性

本文研究了对称集值向量拟均衡问题解集的稳定性.证明了在约束映射满足一定连续性与目标映射是锥-恰当拟凸的集值映射条件下,对称集值向量拟均衡问题的解集是稳定的,还证明了每个对称集值向量拟均衡问题的解集至少存在一个本质连通区.     

n人非合作博弈的轻微利他平衡点

对一类不连续的博弈证明了轻微利他平衡点存在且对这些不连续博弈,如果本质平衡点存在,则他们必是轻微利他平衡点,进而证明了大多数博弈(在Baire分类意义上)是轻微利他的,即它的所有平衡点都是轻微利他的.     

轻微利他弱Pareto-Nash均衡

2008年,Marco和Morgan在正规型博弈中引入轻微利他均衡和友好均衡的概念.利用轻微利他的思想,研究多目标博弈.证明轻微利他弱Pareto-Nash均衡的存在性定理,进一步地讨论轻微利他弱Pareto-Nash均衡和本质均衡的关系.     

Slightly Altruistic Equilibria

We introduce a refinement concept for Nash equilibria (slightly altruistic equilibrium) defined by a limit process and which captures the idea of reciprocal altruism as presented in Binmore (Proceedings of the XV Italian Meeting on Game Theory and Applications, [2003]). Existence is guaranteed for every finite game and for a large class of games with a continuum of strategies. Results and examples emphasize the (lack of) connections with classical refinement concepts. Finally, it is shown that, under a pseudomonotonicity assumption on a particular operator associated to the game, it is possible, by selecting slightly altruistic equilibria, to eliminate those equilibria in which a player can switch to a strategy that is better for the others without leaving the set of equilibria. Part of the results in this paper have been presented at: First Spain, Italy, Netherlands Meeting on Game Theory, Maastricht, 2005; Fifth International ISDG Workshop, Segovia, 2005; GATE, Université Lumière Lyon 2, 2005; XXX AMASES Workshop, Trieste 2006; CSEF, Università di Salerno, 2006.     

Ky Fan点集的本质连通区

本文首先引入了Ｋｙ Ｆａｎ点集本质连能区的概念,证明了对任一满足一定凸性和连续性条件的函数,其Ｋｙ Ｆａｎ点集至少存在一个本质连能区．作为应用,我们推出地任何一般ｎ人非合伯对策（其支付函数满足一些凸性和连续性条件）,其Ｎａｓｈ平衡点集至少存在一个本质连通区．     

Stability of solutions for variational relation problems with applications

In this paper, we prove that most of problems in variational relations (in the sense of Baire category) are essential and that, for any problem in variational relations, there exists at least one essential component of its solution set. As applications, we deduce the existence of essential components of the set of Ky Fan’s points based on Ky Fan’s minimax inequality theorem, the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games, the existence of essential component of the set of solutions for vector Ky Fan’s minimax inequality, the existence of essential components of the set of KKM points and the existence of essential components of the set of solutions for Ky Fan’s section theorem.     

Essential Stability of Solutions for Maximal Element Theorem with Applications

In this paper, we prove that most of problems in maximal element theorem (in the sense of Baire category) are essential and that, for any problem in maximal element theorem, there exists at least one essential component of its solution set. As applications, we deduce the existence of essential components of the set of Ky Fan’s points based on Ky Fan Minimax Inequality, the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games and the existence of essential components of the set of solutions of vector Ky Fan Minimax Inequality.     

Stability of solutions for Ky Fan's section theorem with some applications

In this paper, we prove that “most of” problems in Ky Fan's section theorem (in the sense of Baire category) are essential and that for any problem in Ky Fan's section theorem, there exists at least one essential component of its solution set. As applications, we deduce both the existence of essential components of the set of Ky Fan's points based on Ky Fan's minimax inequality theorem and the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games with non-concave payoffs.     

区间映射的链回归点的可链点集

主要讨论区间映射的链回归点的可链点集与链等价集的关系,证明了:若区间映射的拓扑熵是零,则它的链回归点的可链点集与链等价集相等.此外还得到了区间映射有正拓扑熵的几个等价条件.     

Groups definable in local fields and pseudo-finite fields

Using model-theoretic methods we prove: Theorem A If G is a Nash group over the real or p-adic field, then there is a Nash isomorphism between neighbourhoods of the identity of G and of the set of F-rational points of an algebraic group defined over F. Theorem B Let G be a connected affine Nash group over ℝ. Then G is Nash isogeneous with the (real) connected component of the set of real points of an algebraic group defined over ℝ. Theorem C Let G be a group definable in a pseudo-finite field F. Then G is definably virtually isogeneous with the set of F-rational points of an algebraic group defined over F. Both authors supported by NSF grants.     

A minimally altruistic refinement of Nash equilibrium

We introduce a minimal notion of altruism and use it to refine Nash equilibria in normal form games. We provide three independent existence proofs, relate minimally altruistic Nash equilibrium to other equilibrium concepts, conduct an in-depth sensitivity analysis, and provide examples where minimally altruistic Nash equilibrium leads to improved predictions.