Recently we interpreted the notion of ESS for matrix games under time constraints and investigated the corresponding state in the polymorphic situation. Now we give two further static (monomorphic) characterizations which are the appropriate analogues of those known for classical evolutionary matrix games. Namely, it is verified that an ESS can be described as a neighbourhood invader strategy independently of the dimension of the strategy space in our non-linear situation too, that is, a strategy is an ESS if and only if it is able to invade and completely replace any monomorphic population which totally consists of individuals following a strategy close to the ESS. With the neighbourhood invader property at hand, we establish a dynamic characterization under the replicator dynamics in two dimensions which corresponds to the strong stability concept for classical evolutionary matrix games. Besides, in some special cases, we also prove the stability of the corresponding rest point in higher dimensions.

中文翻译：

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时间约束下演化矩阵博弈的ESS及其与复制器动力学的渐近稳定休息点的关系。

最近，我们解释了时间约束下矩阵游戏的ESS概念，并研究了多态情况下的相应状态。现在我们给出另外两个静态（单态）特征，它们是经典进化矩阵游戏已知特征的适当类似物。即，已经证明，在我们的非线性情况下，ESS也可以被描述为邻域入侵者策略，而与策略空间的大小无关，也就是说，当且仅当策略能够入侵并能够按照接近ESS的策略，完全取代任何完全由个人组成的单态种群。有了附近的入侵者财产，我们在复制器动力学下建立了二维的动态表征，这与经典进化矩阵游戏的强稳定性概念相对应。此外，在某些特殊情况下，我们还证明了相应休息点在更高维度上的稳定性。