On perfectness concepts for bimatrix games

Summary It is shown that the perfect and the proper equilibria for 2×n bimatrix games can be determined systematically by means of the geometric-combinatorial approach of Borm et al. (1988). Moreover, for these games, stable sets and persistent retracts can be characterized. In particular, it is found that each stable set consists of either one or two perfect equilibria, that each stable component contains a proper equilibrium and that each persistent equilibrium is perfect.     

(Pre)kernel catchers for cooperative games

The paper provides a new (pre)kernel catcher in that the relevant set always contains the (pre)kernel. This new (pre)kernel catcher gives rise to a better lower bound _*** such that the kernel is included in strong -cores for all real numbers not smaller than the relevant bound _***.The research for this paper was done under the sponsorship of both the Dutch Organization for the Advancement of Scientific Research (NWO) and the National Science Council (NSC) of Taiwan during a stay of Dr. Chih Chang at the University of Twente, Enschede, The Netherlands.     

Collinearity between the Shapley value and the egalitarian division rules for cooperative games

For each cooperativen-person gamev and eachh{1, 2, ,n}, letv _h be the average worth of coalitions of sizeh andv _h ⁱ the average worth of coalitions of sizeh which do not contain playeriN. The paper introduces the notion of a proportional average worth game (or PAW-game), i.e., the zero-normalized gamev for which there exist numbersc _h such thatv _h –v _h ⁱ =c _h (v _n–1–v _n ^–1/i ) for allh{2, 3, ,n–1}, andiN. The notion of average worth is used to prove a formula for the Shapley value of a PAW-game. It is shown that the Shapley value, the value representing the center of the imputation set, the egalitarian non-separable contribution value and the egalitarian non-average contribution value of a PAW-game are collinear. The class of PAW-games contains strictly the class ofk-coalitional games possessing the collinearity property discussed by Driessen and Funaki (1991). Finally, it is illustrated that the unanimity games and the landlord games are PAW-games.     

On describing the solution sets of generalized Nash games with shared constraints

In this paper we use parametric variational inequality problems for the purpose of describing entire solution sets of generalized Nash games with shared constraints. We prove two theoretical results and we introduce a computational method that practitioners can implement in applied problems modeled as generalized Nash games, under assumptions present in the current literature. Further, we give illustrative examples of how our computational technique is used to derive solution sets of known generalized Nash games previously not solved by existing techniques. We close with the presentation of an applied problem formulated as a generalized Nash game, namely a model of a joint implementation environmental accord between countries. We discuss the possible advantages of modeling it within a generalized Nash game framework.     

关于一类Gauss过程的连续模

本文讨论了一类具有平稳增量的Ｇａｕｓｓ过程｛Ｘ（ｔ），ｔ≥０｝的整体连续模．推广了［１］中关于Ｗｉｅｎｅｒ过程的结果     

Continuity conditions for finite element analysis of solids

In conventional finite element formulations the concept of node—a point where one of the shape functions is unitary and all others are nil—is used to advantage as it simplifies the definition of interelement continuity conditions. This constraint on the definition of the shape functions hinders the formulation of elements with complex shapes and, in particular, of equilibrium elements. In the approach presented herein linearly independent functions are defined within each element irrespectively of the location of the nodes. Interelement continuity conditions are imposed ‘a posteriori’, as in hybrid elements. The derivation of the element matrices is based upon the equations expressing equilibrium, compatibility and the constitutive relations without explicitly using variational principles. This results in a wider choice of available funciiuns ami in an easier way to formulate equilibrium elements and/or to use conforming or non-conforming elements. As the approach used is independent of the choice of basic functions and of the shape of the elements, it is perfectly general. It allows the parallel analysis of kinematically and statically admissible formulations, as proposed by Fraeijs de Veubeke.¹ As the interelement continuity conditions are imposed ‘a posteriori’ new variables are used to express this condition.     

Self-consistent boundary element solution for predicting overall properties of cracked bimaterial solid

In this paper, a self-consistent boundary element method is introduced to predict overall properties of a cracked bimaterial plate. The boundary element (BE) formulation is developed based on Green's function for displacement discontinuity of a bimaterial solid and potential variational principles. The self-consistent method is then introduced into the BE formulation to provide an effective means for estimating overall material constants of a bimaterial solid weakened by cracks. Numerical results for a bimaterial plate with cracks are presented to illustrate the application of the proposed self-consistent BE formulation.     

Permutation games: Another class of totally balanced games

Summary A class of cooperative games in characteristic function form arising from certain sequencing problems and assignment problems, is introduced. It is shown that games of this class are totally balanced. In the proof of this fact we use the Birkhoff-von Neumann theorem on doubly stochastic matrices and the Bondareva-Shapley theorem on balanced games. It turns out that this class of permutation games coincides with the class of totally balanced games if the number of players is smaller than four. For larger games the class of permutation games is a nonconvex subset of the convex cone of totally balanced games.

---

Zusammenfassung Wir führen eine Klasse von kooperativen Spielen in charakteristischer Funktionsform ein, die bei gewissen Folgeproblemen und Zuordnungsproblemen auftreten. Wir zeigen, daß diese Spiele vollständig balanciert sind. Zum Beweis verwenden wir den Satz von Birkhoff-von Neumann über doppelt stochastische Matrizen und den Satz von Bondareva-Shaplex über balancierte Spiele. Es zeigt sich, daß diese Klasse von Permutationsspielen mit der Klasse von vollständig balancierten Spiele übereinstimmt, falls die Zahl der Spieler kleiner als vier ist. Für größere Spiele ist die Klasse der Permutationsspiele eine nichtkonvexe Teilmenge des konvexen Kegels der vollständig balancierten Spiele.

     

AlN-SiC固溶体的制备及介电性能

以碳化硅和铝粉为原料,均匀混合后在不同气氛中于2000℃下保温0.5h制得粉体.用X射线衍射分析(XRD)和扫描电子显微镜(SEM)对其进行表征.同时在8.2～12.4 GHz频率范围内测试其介电性能.结果表明:在N2气氛中,当铝的含量较少时,未出现AlN物相,当铝含量超过10at%时,AlN相开始出现,并且AlN的含量随着铝含量的增加而增加.掺杂铝样品与未掺杂铝样品相比,其介电常数实部ε'和介电损耗tanδ皆降低,且随着铝含量的增加而逐步降低,主要是因为AlN具有较低的介电常数实部和损耗.     

PMTFPSb-PEO-b-PMTFPS含氟三嵌段共聚物的合成及其溶液性质研究

通过阴离子开环聚合制备了Si-H封端聚[1,3,5-三甲基-1,3,5(3,3,3-三氟丙基)硅氧烷](PMTFPS)大分子单体,进而与双烯丙基聚氧乙烯醚(PEO)进行硅氢加成反应合成了不同亲水/疏水嵌段比例的PMTFPS-b-PEO-b-PMTFPS三嵌段共聚物。分别利用GPC和1H-NMR等手段表征了嵌段共聚物的结构组成,测定了不同结构嵌段共聚物的平衡表面张力及临界胶束浓度(cmc)。研究表明,当疏水嵌段链长一定时,临界胶束浓度(cmc)值随聚醚嵌段的增长而下降;当聚醚嵌段长度一定时,cmc值不随疏水嵌段长度的变化而变化。     

连续性在快速成形中的应用

将实体几何连续性应用于快速分层,可以降低内存,加快信息提取时间.另外,沿垂直于z向将巨型STL格式文件分割成多个STL格式文件,依次成形,可以避免巨型STL格式文件的读入错误和手工粘结带来的误差,提高了制件精度.     

Calcium hydroxyapatites: evaluation of sorption properties for cadmium ions in aqueous solution

The efficiency and mechanisms of cadmium sorption on two synthetic calcium hydroxyapatites from aqueous solution were investigated. Both hydroxyapatites remove cadmium from aqueous solutions with an efficiency higher than 99.5% at pH 5–6.The mechanisms of cadmium sorption were studied using batch experiments, X-ray diffraction, scanning electron microscopy and nuclear microprobe. Cadmium is incorporated into the hydroxyapatite structure via diffusion and ion exchange. Once cadmium is sorbed, cadmium-containing hydroxyapatites can be separated from the liquid phase by flocculation. Thus hydroxyapatite can potentially be used for remediating contaminated water and industrial wastes. The fact that cadmium is incorporated into the bulk of the apatite is important in the context of the safe storage of used sorbent material.     

Decomposition of games with non-empty core into veto-controlled simple games

Summary The non-negative games with non-empty core form a polyhedral cone. Extreme directions of this convex cone correspond to veto-controlled simple games. In this paper a constructive method is described to represent a non-negative game with non-empty core as a positive linear combination of veto-controlled simple games. As an application a constructive proof is suggested of a result of Spinetto (see [5]) dealing with the extreme points of the compact and convex set of nonnegative (0, 1)-normalized games with non-empty core.

---

Zusammenfassung Die nicht-negativen Spiele mit nichtleerem Kern bilden einen polyedrischen Kegel. Extreme Richtungen dieses konvexen Kegels korrespondieren mit Veto-kontrollierten einfachen Spielen. In diesem Beitrag wird eine konstruktive Methode beschrieben, mit der ein nicht-negatives Spiel mit nicht-leerem Kern als eine positive Linearkombination Veto-kontrollierter einfacher Spiele repräsentiert werden kann. Als eine Anwendung wird ein konstruktiver Beweis eines Resultats von Spinetto [5] vorgeschlagen, das von den Extremalpunkten der kompakten und konvexen Menge nicht-negativer (0, 1)-normalisierter Spiele mit nichtleerem Kern handelt.

     

A generalization of an oddness-theorem for bimatrix games

Summary It is a well-known result of Lemke and Howson that the number of Nash-equilibria of a bimatrix game is odd in a nondegenerate case. In this paper a generalized version of this theorem will be proved. It will be shown that in case of finiteness of the number of Nash-equilibria the number of nondegenerate Nash-equilibria is always odd. Consequences of this fact are nondegeneracy for unique Nash-equilibria and some results of Jansen.

---

Zusammenfassung Ein bekanntes Resultat von Lemke und Howson besagt, daß die Anzahl der Nash-Gleichgewichtungspunkte für nichtdegenerierte Bimatrix-Spiele ungerade ist. Dieses Ergebnis wird im folgenden Sinne verallgemeinert: es wird nachgewiesen, daß die Anzahl der nichtdegenerierten Gleichgewichtspunkte für Spiele mit höchstens endlich vielen Gleichgewichtspunkten stets ungerade ist. Daraus ergibt sich, daß eindeutige Gleichgewichtspunkte nichtdegeneriert sind. Außerdem erhält man damit erneut einige auf Jansen zurückgehende Resultate.