论文标题
逆最大定理和一些后果
Inverse maximum theorems and some consequences
论文作者
论文摘要
我们处理倒数定理，这些定理的灵感来自Aoyama，Komiya，Li等人，Park和Komiya和Yamauchi。由于我们的结果，我们指出并证明了逆最大NASH定理，并表明在适当的假设下，任何通用的NASH游戏都可以简化为经典的NASH游戏。此外，我们表明，Arrow和Debreu的结果是关于通用NASH游戏的解决方案的结果，实际上等同于Debreu-Fan-Glicksberg为古典NASH游戏提供的结果，这反过来又等同于Kakutani-Fan-Fan-fan-Glisckberg的固定点。
We deal with inverse maximum theorems, which are inspired by the ones given by Aoyama, Komiya, Li et al., Park and Komiya, and Yamauchi. As a consequence of our results, we state and prove an inverse maximum Nash theorem and show that any generalized Nash game can be reduced to a classical Nash game, under suitable assumptions. Additionally, we show that a result by Arrow and Debreu, on the existence of solutions for generalized Nash games, is actually equivalent to the one given by Debreu-Fan-Glicksberg for classical Nash games, which in turn is equivalent to Kakutani-Fan-Glisckberg's fixed point theorem.
