Equilibria for Pooling Situations

This paper deals with pooling situations, which can be considered as exchange economies with indivisible goods and money, and two related cooperative games which we refer to as pooling games with individual rights and pooling games without individual rights. It is shown that the classes of pooling games without individual rights and transportation games coincide and are contained in the class of pooling games with individual rights. With tools from discrete convexity theory, it is proved that competitive equilibria for pooling situations exist. As a consequence, an alternative proof of the nonemptiness of the core of pooling games is provided.     

Type monotonic allocation schemes for a class of market games

We consider an extension of glove markets, called T-markets, characterize a family of weighted allocation rules, and define related cooperative games. For the class of T-market games we introduce a new solution concept called the type monotonic allocation scheme. It turns out that the nucleolus and the τ-value generate the same type monotonic allocation scheme with nice extra properties. Initial research for this paper was supported by the Hungarian Scientific Research Fund grant OTKA T030945. The authors thank Ruud Hendrickx for his valuable comments. Research of T. Solymosi was also supported in part by OTKA grant T046194.     

Multicriteria games and potentials

In this note we study how far the theory of strategic games with potentials, as reported by Monderer and Shapley (Games Econ Behav 14:124–143, 1996), can be extended to strategic games with vector payoffs, as reported by Shapley (Nav Res Logist Q 6:57–61, 1959). The problem of the existence of pure approximate Pareto equilibria for multicriteria potential games is also studied.      

On the determinateness of semi-infinite bimatrix games

In this paper it is shown that every 2 × ∞ bimatrix game is weakly determined. For the proof of this fact we introduce ?-optimal andk-guaranteeing points for a convex set in IR ^m and a labeling technique which is typical for 2 × ∞ bimatrix games.     

Linear production with transport of products,resources and technology

This paper considers linear production situations with a finite number of production facilities, each with its own production technology and market prices. The economic agents control resources at the different facilities. Transport of resources, products and technology is restricted. Sufficient conditions for the corresponding TU-game to be balanced are discussed. In this we extend the results of Owen (1975), Granot (1986) and Curiel, Derks, and Tijs (1989). An example is presented in some detail.This research is sponsored by the Foundation for the Promotion of Research in Economic Sciences, which is part of the Dutch Organization for Scientific Research (NWO).     

Stochastic Arithmetic in Multiprecision

Floating-point arithmetic precision is limited in length the IEEE single (respectively double) precision format is 32-bit (respectively 64-bit) long. Extended precision formats can be up to 128-bit long. However some problems require a longer floating-point format, because of round-off errors. Such problems are usually solved in arbitrary precision, but round-off errors still occur and must be controlled. Interval arithmetic has been implemented in arbitrary precision, for instance in the MPFI library. Interval arithmetic provides guaranteed results, but it is not well suited for the validation of huge applications. The CADNA library estimates round-off error propagation using stochastic arithmetic. CADNA has enabled the numerical validation of real-life applications, but it can be used in single precision or in double precision only. In this paper, we present a library called SAM (Stochastic Arithmetic in Multiprecision). It is a multiprecision extension of the classic CADNA library. In SAM (as in CADNA), the arithmetic and relational operators are overloaded in order to be able to deal with stochastic numbers. As a consequence, the use of SAM in a scientific code needs only few modifications. This new library SAM makes it possible to dynamically control the numerical methods used and more particularly to determine the optimal number of iterations in an iterative process. We present some applications of SAM in the numerical validation of chaotic systems modeled by the logistic map.     

Structure and impact resistance of short carbon fiber reinforced polyamide 6 composites

Short carbon fiber (CF) reinforced polyamide 6 (PA6) composites were prepared by homogenization of the components in a twin-screw extruder and by injection molding. Fiber content was varied between 0 and 16 vol%, while specimens were injection molded at rates between 2.0 and 22.6 cm/s. Average fiber length and orientation were measured to characterize structure. Average fiber length decreased with increasing fiber content and processing rate. The observed structure is contradictory to those reported in the literature for short glass fiber reinforced composites. Fibers were oriented randomly relative to the mold fill direction in the skin layer, while they were oriented parallel to this direction in the middle of the specimen. The thickness of the skin decreased with increasing injection rate and decreasing fiber content. Although instrumented impact testing indicated brittle failure at all combinations of the variables, the strain energy release rate could not be determined by the usual technique using varying notch depths because of the different properties of the skin and the core. Also, the mechanism of failure seems to be different in the two layers. A minimum appears in the fracture toughness and impact resistance at low fiber contents, indicating that fibers might promote fracture initiation at such compositions. Fiber length changed in a narrow range in the studied composites; thus, properties are determined mainly by orientation. As a consequence, both increased fiber content and injection rate lead to an increase of stiffness and toughness.     

Convex multi-choice games: Characterizations and monotonic allocation schemes

This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Furthermore, level-increase monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is extendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game.     

A study on Fe+ centers in NaCl crystals

An ESR study on Fe⁺ centers in NaCl at sites with various symmetries is presented. Such centers, with axial, octahedral or orthorhombic symmetry, can be observed below 32 K, in crystals freshly quenched at RT, before irradiating at 77 K. On warming to 180 K the conversion of Fe⁺ (orthorhombic) to Fe⁺ (axial) occurs. A second conversion of Fe⁺ (axial) to Fe⁺ (octahedral) takes place at 220 K. Both conversions are due to the tendency of the positive-ion vacancy to move away from the Fe⁺ ions.