Robust Nash equilibria in vector-valued games with uncertainty
Robust Nash equilibria in vector-valued games with uncertainty
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DOI：
10.1007/s10479-020-03563-2
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发表时间：
2020-03
影响因子：
4.8
通讯作者：
G. Crespi;Daishi Kuroiwa;M. Rocca
中科院分区：
文献类型：
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作者：
G. Crespi;Daishi Kuroiwa;M. Rocca
我们研究了支付函数具有不确定性的向量值博弈。我们减少了纳什均衡的概念，一个强大的集优化问题，我们相应地定义了强大的纳什均衡和弱强大的纳什均衡的概念。证明了后者的存在性结果，并将前者与Yu和Liu（J Optim Theory Appl 159：272-280，2013）中的类似概念进行了比较。弱鲁棒纳什均衡的拟议定义比Yu和Liu（2013）中已经引入的定义要弱。相反，我们引入的鲁棒纳什均衡与Yu和Liu（2013）中的鲁棒均衡概念不可比较，后者是按分量定义的。然而，通过一个例子，我们表明，我们的概念有一些优点，避免了一些陷阱，发生与其他。
We study a vector-valued game with uncertainty in the pay-off functions. We reduce the notion of Nash equilibrium to a robust set optimization problem and we define accordingly the notions of robust Nash equilibria and weak robust Nash equilibria. Existence results for the latter are proved and a comparison between the former and the analogous notion in Yu and Liu (J Optim Theory Appl 159:272–280, 2013) is shown with an example. The proposed definition of weak robust Nash equilibrium is weaker than that already introduced in Yu and Liu (2013). On the contrary, the robust Nash equilibrium we introduce is not comparable with the notion of robust equilibrium in Yu and Liu (2013), that is defined componentwise. Nevertheless, by means of an example, we show that our notion has some advantages, avoiding some pitfalls that occurs with the other.