A coalition formation value for games in partition function form

The coalition formation problem in an economy with externalities can be adequately modeled by using games in partition function form (PFF games), proposed by Thrall and Lucas. If we suppose that forming the grand coalition generates the largest total surplus, a central question is how to allocate the worth of the grand coalition to each player, i.e., how to find an adequate solution concept, taking into account the whole process of coalition formation. We propose in this paper the original concepts of scenario-value, process-value and coalition formation value, which represent the average contribution of players in a scenario (a particular sequence of coalitions within a given coalition formation process), in a process (a sequence of partitions of the society), and in the whole (all processes being taken into account), respectively. We give also two axiomatizations of our coalition formation value.     

Applying relational algebra and RelView to coalition formation

We present an application of relational algebra to coalition formation. This leads to specifications, which can be executed with the help of the RelView tool after a simple translation into the tool’s programming language. As an example we consider a simplification of the situation in Poland after the 2001 elections.     

Two new algorithms for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities

This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made.     

The structure of stratified systems and the structure of mobility: A first approximation to a structural theory of vertical mobility

This essay summarizes an inquiry that explores relations between the structure of stratified systems and the processes of vertical mobility. The inquiry considers economic stratification (the distribution of wealth) and is directed to determining whether the structural properties of stratification systems are sufficient to generate basic patterns in vertical mobility observed in empirical research, especially, the rank‐distance effect. In particular, the question is whether these patterns can be generated even if movement is constrained by nothing more than the size of the population over which wealth is distributed and the total amount of wealth to be distributed. Our results show that the rank‐distance effect emerges even under these minimal assumptions and, further, that rates and distances of vertical mobility are closely related to changes in these boundary parameters of a stratified system. The basic theory developed to relate structure and mobility provides results that are highly consistent with many empirical observations. It also challenges existing claims concerning the nature of the mechanisms determining the relative status immobility of most people in large scale systems. The theory implies that the way in which system structure constrains opportunity for movement is, by itself, sufficient to produce this result and others commonly observed.     

Approximate cores of replica games and economies: Part II: Set-up costs and firm formation in coalition production economies

A model of a coalition production economy allowing set-up costs, indivisibilities,and nonconvexities is developed. It is shown that for all sufficiently large replications, approximate cores of the economy are nonempty.     

Multiple-Load Truss Topology and Sizing Optimization: Some Properties of Minimax Compliance

This paper considers the mathematical properties of discrete or discretized mechanical structures under multiple loadings which are optimal w.r.t. maximal stiffness. We state a topology and/or sizing problem of maximum stiffness design in terms of element volumes and displacements. Multiple loads are handled by minimizing the maximum of compliance of all load cases, i.e., minimizing the maximal sum of displacements along an applied force. Generally, the problem considered may contain constraints on the design variables. This optimization problem is first reformulated in terms of only design variables. Elastic equilibrium is hidden in potential energy terms. It is shown that this transformed objective function is convex and continuous, including infinite values. We deduce that maximum stiffness structures are dependent continuously on the bounds of the element volumes as parameters. Consequently, solutions to sizing problems with small positive lower bounds on the design variables can be considered as good approximations of solutions to topology problems with zero lower bounds. This justifies heuristic approaches such as the well-known stress-rationing method for solving truss topology problems.     

Independence of inadmissible strategies and best reply stability: a direct proof

Hillas (1990) introduced a definition of strategic stability based on perturbations of the best reply correspondence that satisfies all of the requirements given by Kohlberg and Mertens (1986). Hillas et al. (2001) point out though that the proofs of the iterated dominance and forward induction properties were not correct. They also provide a proof of the IIS property, a stronger version of both iterated dominance and forward induction, using the results of that paper. In this note we provide a direct proof of the IIS property.Received February 2002     

On the joint distribution of surplus before and after ruin under a Markovian regime switching model

We consider a Markovian regime switching insurance risk model (also called Markov-modulated risk model). The closed form solutions for the joint distribution of surplus before and after ruin when the initial surplus is zero or when the claim size distributions are phase-type distributed are obtained.     

Optimization of the Norm of a Vector-Valued DC Function and Applications

In this paper, we show that a DC representation can be obtained explicitly for the composition of a gauge with a DC mapping, so that the optimization of certain functions involving terms of this kind can be made by using standard DC optimization techniques. Applications to facility location theory and multiple-criteria decision making are presented.     

两个凸多面体的差及几种次微分之间的关系

给出两种两个凸多面体差的表达式,利用这些表达式,可以具体计算这两种凸多面体的差,做为应用讨论了利用拟微分计算Penot微分和Clarke广义梯度,特别讨论了一类非光滑函数,极大值函数的光滑复合。     

On the restricted cores and the bounded core of games on distributive lattices

A game with precedence constraints is a TU game with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. Its core may be unbounded, and the bounded core, which is the union of all bounded faces of the core, proves to be a useful solution concept in the framework of games with precedence constraints. Replacing the inequalities that define the core by equations for a collection of coalitions results in a face of the core. A collection of coalitions is called normal if its resulting face is bounded. The bounded core is the union of all faces corresponding to minimal normal collections. We show that two faces corresponding to distinct normal collections may be distinct. Moreover, we prove that for superadditive games and convex games only intersecting and nested minimal collection, respectively, are necessary. Finally, it is shown that the faces corresponding to pairwise distinct nested normal collections may be pairwise distinct, and we provide a means to generate all such collections.     

Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations

In this paper, we consider two distinct classes of network problems – financial networks with intermediation and with electronic transactions and transportation network equilibrium problems, which have been modeled and studied independently. We then prove that the former problem can be reformulated as the latter problem through an appropriately constructed abstract network i.e., a supernetwork. The established equivalence allows one to then transfer the methodological tools, in particular, algorithms, that have been developed for transportation network equilibria to the financial network domain. In addition, this connection provides us with a novel interpretation of the financial network equilibrium conditions in terms of paths and path flows and a direct existence result. We further show how the theoretical results obtained in this paper can be exploited computationally through several numerical examples.      

Equilibrium model of a credit market: Statement of the problem and solution methods

An equilibrium model of a credit market is proposed and examined. The credit price or the interest rate in the model is determined by the consistent interaction of two macroscopic factors: supply and demand. Methods for computing an equilibrium interest rate are suggested. The methods are interpreted as market-balancing dynamics. The convergence of the methods is proved.     

网络计划优化技术中顺序优化的编程模式与算法设计

网络计划优化技术中的顺序优化理论具有国际先进水平，已有十多年的历史，但因编程困难，始终未能和实际有效地结合起来。顺序优化的编程是相当复杂的，之所以复杂是因为它不仅包含顺序优化，而且还包含因顺序优化而带来的网络图的调整。本就是针对这一情况，介绍了一种适合解决此类问题的方法。     

Maximization of the lift/drag ratio of airfoils with a turbulent boundary layer: Sharp estimates,approximation, and numerical solutions

The lift/drag ratio of an airfoil placed in an incompressible attached flow is maximized taking into account the viscosity in the boundary-layer approximation. An exact solution is constructed. The situation when the resulting solutions are not in the admissible class of univalent flows is discussed. A procedure is proposed for determining physically feasible airfoils (with a univalent flow region) with a high lift/drag ratio. For this purpose, a class of airfoils is constructed that are determined by a twoparameter function approximating the found exact solution to the variational problem. For this class, the ranges of free parameters leading to physically feasible flows are found. The results are verified by computing a turbulent boundary layer using Eppler’s method, and airfoils with a high lift/drag ratio in an attached flow are detected.