Type space on a purely measurable parameter space

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Hars´anyi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players

Operator means of probability measures and generalized Karcher equations

In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a large part of Kubo-Ando theory to arbitrary many variables, in fact, to the case of probability measures with bounded support on the cone of positive definite operators. This framework characterizes each operator mean extrinsically as unique solutions of generalized Karcher equations which are obtained by exchanging the matrix logarithm function in the Karcher equation to arbitrary operator monotone functions over the positive real half-line. If the underlying Hilbert space is finite dimensional, then these generalized Karcher equations are Riemannian gradients of convex combinations of strictly geodesically convex log-determinant divergence functions, hence these new means are the global minimizers of them, in analogue to the case of the Karcher mean as pointed out. Our framework is based on fundamental contraction results with respect to the Thompson metric, which provides us nonlinear contraction semigroups in the cone of positive definite operators that form a decreasing net approximating these operator means in the strong topology from above.Comment: arXiv admin note: text overlap with arXiv:1208.560

On the completeness of the universal knowledge-belief space

Meier (2008) shows that the universal knowledge-belief space exists. However, besides the universality there is an other important property might be imposed on knowledge-belief spaces, inherited also from type spaces, the completeness. In this paper we introduce the notion of complete knowledge-belief space, and demonstrate that the universal knowledge-belief space is not complete, that is, some subjective beliefs (probability measures) on the universal knowledge-belief space are not knowledge-belief types

Recent Achievements in Numerical Simulation in Sheet Metal Forming Processes

Purpose of this paper: During the recent 10-15 years, Computer Aided Process Planning and Die Design evolved as one of the most important engineering tools in sheet metal forming, particularly in the automotive industry. This emerging role is strongly emphasized by the rapid development of Finite Element Modelling, as well. The purpose of this paper is to give a general overview about the recent achievements in this very important field of sheet metal forming and to introduce some special results in this development activity. Design/methodology/approach: Concerning the CAE activities in sheet metal forming, there are two main approaches: one of them may be regarded as knowledge based process planning, whilst the other as simulation based process planning. The author attempts to integrate these two separate developments in knowledge and simulation based approach by linking commercial CAD and FEM systems. Findings: Applying the above approach a more powerful and efficient process planning and die design solution can be achieved radically reducing the time and cost of product development cycle and improving product quality. Research limitations: Due to the different modelling approaches in CAD and FEM systems, the biggest challenge is to enhance the robustness of data exchange capabilities between various systems to provide an even more streamlined information flow. Practical implications: The proposed integrated solutions have great practical importance to improve the global competitiveness of sheet metal forming in the very important segment of industry. Originality/value: The concept described in this paper may have specific value both for process planning and die design engineers