Iterated Strict Dominance in General Games

We offer a definition of iterated elimination of strictly dominated strategies (IESDS) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS by means of a "stability" criterion, and offer a sufficient and necessary epistemic condition for IESDS. We show by an example that IESDS may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS preserves the set of Nash equilibria. Nous donnons une définition de l’élimination itérative des stratégies qui sont strictement donimées (EISSD) pour les jeux avec un nombre fini (ou infini) de joueurs , des ensembles de stratégies compactes (ou non-compactes), et des fonctions de gains continues (ou non-continues). Le processus EISSD est bien défini et indépendant de l’ordre d’élimination. Nous donnons une caractérisation du processus EISSD en utilisant un critère de stabilité et offrons une condition épistémologique. Nous démontrons que le processus EISSD peut produire des équilibres faux dans la classe des jeux de meilleures réponses sécuritaires de Reny. Nous donnons des conditions nécessaires et suffisantes pour que le processus EISSD conserve l’ensemble des équilibre de Nash.game theory, strict dominance, iterated elimination, Nash equilibrium, Reny's better-reply secure games., théorie des jeux, dominance stricte, élimination itérative, équilibre de Nash, jeux de meilleures réponses sécuritaires de Reny

Existence and asymptotic behavior of least energy sign-changing solutions for Schrodinger-Poisson systems with doubly critical exponents

In this paper, we are concerned with the following Schr\"{o}dinger-Poisson system with critical nonlinearity and critical nonlocal term due to the Hardy-Littlewood-Sobolev inequality \begin{equation}\begin{cases} -\Delta u+u+\lambda\phi |u|^3u =|u|^4u+ |u|^{q-2}u,\ \ &\ x \in \mathbb{R}^{3},\\[2mm] -\Delta \phi=|u|^5, \ \ &\ x \in \mathbb{R}^{3}, \end{cases} \end{equation} where $\lambda\in \mathbb{R}$ is a parameter and $q\in(2,6)$. If $\lambda\ge (\frac{q+2}{8})^2$ and $q\in(2,6)$, the above system has no nontrivial solution. If $\lambda\in (\lambda^*,0)$ for some $\lambda^*<0$, we obtain a least energy radial sign-changing solution $u_\lambda$ to the above system. Furthermore, we consider $\lambda$ as a parameter and analyze the asymptotic behavior of $u_\lambda$ as $\lambda\to 0^-$

Optically-Nonactive Assorted Helices Array with Interchangeable Magnetic/Electric Resonance

We report here the designing of optically-nonactive metamaterial by assembling metallic helices with different chirality. With linearly polarized incident light, pure electric or magnetic resonance can be selectively realized, which leads to negative permittivity or negative permeability accordingly. Further, we show that pure electric or magnetic resonance can be interchanged at the same frequency band by merely changing the polarization of incident light for 90 degrees. This design demonstrates a unique approach to construct metamaterial.Comment: 15 pages, 4 figure

Anderson Impurity in Helical Metal

We use a trial wave function to study the spin-1/2 Kondo effect of a helical metal on the surface of a three-dimensional topological insulator. While the impurity spin is quenched by conduction electrons, the spin-spin correlation of the conduction electron and impurity is strongly anisotropic in both spin and spatial spaces. As a result of strong spin-orbit coupling, the out-of-plane component of the impurity spin is found to be fully screened by the orbital angular momentum of the conduction electrons.Comment: The published versio