On pure equilibria for bimatrix games

In Shapley (1964) several conditions are given for the existence of pure saddlepoints for a matrix game. In this paper we show that only a few of these conditions, when translated to the situation of a bimatrix game guarantee the existence of pure equilibria. Further, we associate with a bimatrix game a directed graph as well as a so-called binary game. If this graph has no cycles, then the bimatrix game in question has a pure equilibrium. It is shown that the binary game for a bimatrix game without a pure equilibrium possesses a fundamental subgame, which can be characterized by means of minimal cycles.     

A vertex oriented approach to the equal remaining obligations rule for minimum cost spanning tree situations

In this paper, we consider spanning tree situations, where players want to be connected to a source as cheap as possible. These situations involve the construction of a spanning tree with the minimum cost as well as the allocation of the cost of this minimum cost spanning tree among its users in a fair way. Feltkamp, Muto and Tijs 1994 introduced the equal remaining obligations rule to solve the cost allocation problem in these situations. Recently, it has been shown that the equal remaining obligations rule satisfies many appealing properties and can be obtained with different approaches. In this paper, we provide a new approach to obtain the equal remaining obligations rule. Specifically, we show that the equal remaining obligations rule can be obtained as the average of the cost allocations provided by a vertex oriented construct-and-charge procedure for each order of players.     

Determination of <Superscript>237</Superscript>Np, <Superscript>93</Superscript>Zr and other long-lived radionuclides in medium and low level radioactive waste samples

The majority of long-lived radionuclides produced in the nuclear fuel cycle can be regarded as “difficult-to-measure” nuclides, hence chemical separation is needed before the nuclear measurement of them. A combined radiochemical procedure that enables the simultaneous determination of some “difficult-to-measure” nuclides in medium and low level radioactive wastes has been developed in our laboratory. Recently, this method has been extended for determination of ²³⁷Np and ⁹³Zr. ²³⁷Np and ⁹³Zr are pre-concentrated by co-precipitation on iron(II) hydroxide and zirconium oxide, separated by extraction chromatography using UTEVA, and measured by inductively coupled plasma mass spectrometry (ICP-MS). As even traces of polyatomic ions and isotopes at m/z 237 or 93 cause considerable interferences during ICP-MS detection, a purification step by extraction chromatography was needed. Analyzing real samples (evaporation concentrates of a nuclear power plant) 66–99% and 31–99% chemical yields were achieved for Np and Zr, respectively.     

Dynamics of Au-induced nanowires on Ge(001)

We have studied the dynamics of Au-induced nanowires on Ge(001) using scanning tunnelling microscopy. The ridges of these nanowires consist of buckled dimers that have their dimer bond aligned in a direction perpendicular to the nanowire direction. Neighbouring dimers have a preference to buckle in an opposite direction, leading to rows with a zigzag appearance. Dimers located at anti-phase boundaries continuously flip back and forth between their two buckled configurations. This process is thermally induced and occurs at an average frequency of 25 Hz at room temperature.     

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.