Farsighted coalitional stability in TU-games

We study farsighted coalitional stability in the context of TU-games. We show that every TU-game has a nonempty largest consistent set and that each TU-game has a von Neumann–Morgenstern farsighted stable set. We characterize the collection of von Neumann–Morgenstern farsighted stable sets. We also show that the farsighted core is either empty or equal to the set of imputations of the game. In the last section, we explore the stability of the Shapley value. The Shapley value of a superadditive game is a stable imputation: it is a core imputation or it constitutes a von Neumann–Morgenstern farsighted stable set. A necessary and sufficient condition for a superadditive game to have the Shapley value in the largest consistent set is given.     

Farsighted stable sets in Hotelling’s location games

We apply the farsighted stable set to two versions of Hotelling’s location games: one with a linear market and another with a circular market. It is shown that there always exists a farsighted stable set in both games, which consists of location profiles that yield equal payoff to all players. This stable set contains location profiles that reflect minimum differentiation as well as those profiles that reflect local monopoly. These results are in contrast to those obtained in the literature that use some variant of Nash equilibrium. While this stable set is unique when the number of players is two, uniqueness no longer holds for both models when the number of players is at least three.     

Deadlock free buffer allocation in closed queueing networks

Blocking queueing networks are of much interest in performance analysis due to their realistic modeling capability. One important feature of such networks is that they may have deadlocks which can occur if the node capacities are not sufficiently large. A necessary and sufficient condition for the node capacities is presented such that the network is deadlock free. An algorithm is given for buffer allocation in blocking queueing networks such that no deadlocks will occur assuming that the network has the special structure called cacti-graph. Additional algorithm which takes linear time in the number of nodes, is presented to find cycles in cacti networks.Akyildiz's work was supported in part by School of Information and Computer Science, ICS, of Georgia Tech and by the Air Force Office of the Scientific Research (AFOSR) under Grant AFOSR-88-0028.     

The average path length of scale free networks

In this paper, the exact solution of average path length in Barabási–Albert model is given. The average path length is an important property of networks and attracts much attention in many areas. The Barabási–Albert model, also called scale free model, is a popular model used in modeling real systems. Hence it is valuable for us to examine the average path length of scale free model. There are two answers, regarding the exact solution for the average path length of scale free networks, already provided by Newman and Bollobas respectively. As Newman proposed, the average path length grows as log(n) with the network size n. However, Bollobas suggested that while it was true when m = 1, the answer changed to log(n)/log(log(n)) when m > 1. In this paper, as we propose, the exact solution of average path length of BA model should approach log(n)/log(log(n)) regardless the value of m. Finally, the simulation is presented to show the validity of our result.     

Optimal design of hierarchical networks with free main path extremes

We propose an optimal, two-stage procedure for the optimal design of minimum cost hierarchical spanning networks, consisting of a main path and secondary trees. The optimal location of the origin and destination nodes of the path is also found. We test our procedure and compare it with a known method.     

Universal robustness of scale‐free networks against cascading edge failures

Considering the effect of the local topology structure of an edge on cascading failures, we investigate the cascading reaction behaviors on scale‐free networks with respect to small edge‐based initial attacks. Adopt the initial load of an edge ij in a network to be L_ij = (k_ik_j)^α[(∑k_a)(∑k_b)]^β with k_i and k_j being the degrees of the nodes connected by the edge ij, where α and β are tunable parameters, governing the strength of the edge initial load, and Γ_i and Γ_j are the sets of neighboring nodes of i and j, respectively. Our aim is to explore the relationship between some parameters and universal robustness characteristics against cascading failures on scale‐free networks. We find by the theoretical analysis that the Baraba'si‐Albert (BA) scale‐free networks can reach the strongest robustness level against cascading failures when α + β = 1, where the robustness is quantified by a transition from normal state to collapse. And the network robustness has a positive correlation with the average degree. We furthermore confirm by the numerical simulations these results.     

Neural networks analysis of free laminar convection heat transfer in a partitioned enclosure

The feasibility of using neural networks (NNs) to predict the complete thermal and flow variables throughout a complicated domain, due to free convection, is demonstrated. Attention is focused on steady, laminar, two-dimensional, natural convective flow within a partitioned cavity. The objective is to use NN (trained on a database generated by a CFD analysis of the problem of a partitioned enclosure) to predict new cases; thus saving effort and computation time. Three types of NN are evaluated, namely General Regression NNs, Polynomial NNs, and a versatile design of Backpropagation neural networks. An important aspect of the study was optimizing network architecture in order to achieve best performance. For each of the three different NN architectures evaluated, parametric studies were performed to determine network parameters that best predict the flow variables.A CFD simulation software was used to generate a database that covered the range of Rayleigh number Ra = 10⁴–5 × 10⁶. The software was used to calculate the temperature, the pressure, and the horizontal and vertical components of flow speed. The results of the CFD were used for training and testing the neural networks (NN). The robustness of the trained NNs was tested by applying them to a “production” data set (1500 patterns for Ra = 8 × 10⁴ and 1500 patterns for Ra = 3 × 10⁶), which the networks have never been “seen” before. The results of applying the technique on the “production” data set show excellent prediction when the NNs are properly designed. The success of the NN in accurately predicting free convection in partitioned enclosures should help reduce analysis-time and effort. Neural networks could potentially help solve some cases in which CFD fails to solve because of numerical instability.     

On centripetal flows of entities in scale‐free networks with nodes of finite capability

We examine the transmission of entities from the peripheries of scale‐free networks toward their centers when the nodes of the network have finite processing capabilities. We look at varying network utilization, U and find that clogging of the network sets in after a threshold value has been exceeded, and that the congestion sets in at the downstream nodes (those nearer to the collector) having large numbers of upstream neighbors. Investigation of the question of the degree of correlation of several characteristics of scale‐free networks (such as the average path length to the collector <l_(min)> and the average clustering coefficient ) with the dynamics of centripetal flow in them reveals a negative answer: any correlation is indirect and will manifest in the number of producer nodes (which dictate the effective heaviness of the flow) and the interconnectedness of the feeder nodes, those nodes which are immediate neighbors of the collector node. An examination of reinforcement strategies shows dramatic improvements in both the finishing rate, and the average total transmission time, when the more centrally‐placed nodes are reinforced first, showing that the entities spend a large amount of their lifetime waiting in line at those nodes (which constitute the bottlenecks in the network) compared to the nodes in the periphery. Our results reinforce the importance of a network's hubs and their immediate environs, and suggest strategies for prioritizing elements of a network for optimization. © 2014 Wiley Periodicals, Inc. Complexity 21: 283–295, 2015     

Juche in international trade

We show that in trade between two parties, one of whom has much greater endowment that the other, calculated by the Nash bargaining solution, tends to exploit the poorer party, as compared with the competitive equilibrium. This can be interpreted as saying that trade between a developed country and a developing nation, each acting on the basis of self-interest, will result in exploitation of the developing nation. This illustrates one aspect of the idea of Juche. We also show that if trade in two goods among two parties is extended to a third, one of the two parties will be worse off as a result under natural hypotheses. This can be interpreted as explaining why trade between a developing country and a developed country might make some groups in the developing country rich but other groups poor, a second aspect of Juche.     

基于网络分析方法的国际贸易问题研究

本文基于网络分析方法研究贸易问题.首先利用网络特征分析考察贸易规模变化以及经济主体的地位变化问题,然后提出动态指数随机图模型来研究影响因素对贸易的影响程度变化问题.结果表明:2001年-2016年国际贸易规模总体上是扩大的;美国和德国在进出口市场上长期占有主导地位,中国是贸易关系增长最快的国家,国际地位上升明显;单边贸易对双边贸易的促进作用在经济景气时更为显著, GDP对出口的促进作用变化较进口更为明显,距离对贸易的抑制作用变化程度较小.     

贸易信用的未来

18个月前,使用贸易信用保险的公司还很少,他们中的大多数甚至还不了解贸易信用保险的真正价值所在。贸易信用保险是帮助贸易商规避坏账风险的工具。你不能指望一个评级机构会为其评级的差错提供赔偿。     

The intersection of free submonoids of a free monoid is free

Several necessary and sufficient conditions exist for a submonoid of a free monoid to be free. For a few, see [1] through [6]. This short note uses one of these conditions, due to Schützenberger (see [2], p. 119, or [4], Theorem 1.4) to establish that the intersection of free submonoids of a free monoid M is again free. Schützenberger's condition is also proven in this note.     

Stably free modules over virtually free groups

Let F _m be the free group on m generators, and let G be a finite nilpotent group of non square-free order; we show that for each m ≥ 2 the integral group ring Z[G × F _m ] has infinitely many stably free modules of rank 1.     

Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk

In practice, to attract new buyers and to avoid lasting price competition, a seller frequently offers its buyers a permissible delay in payment (ie, trade credit). However, the policy of granting a permissible delay in payment adds an additional dimension of default risk to the seller. In contrast to previous researchers for finding optimal solutions to buyers, we first propose an economic order quantity model from the seller's prospective to determine its optimal trade credit and order quantity simultaneously. In addition, we incorporate the important and relevant fact that trade credit has a positive impact on demand rate but a negative impact on receiving the buyer's debt obligations. Then the necessary and sufficient conditions to obtain the seller's optimal trade credit and order quantity are derived. An algorithm to determine the seller's optimal trade credit is also proposed. Finally, we use some numerical examples to illustrate the theoretical results and to provide some managerial insights.     

Delineating store trade areas through morphological analysis

The precise knowledge of trade area limits is of importance for companies that want to accurately fit their marketing strategy to local features. Many methods have been already proposed in the literature but either they are too simple or often are at the same time approximate and expensive in computer times. This paper develops the framework of a new method based on mathematical morphology, a science usually used in image processing but not yet applied on data resulting from management sources. This method applied to the delineation of a trade area breaks up the acquisition of the data, filtering, segmentation and regularization of the area boundaries.     

Path-isomorphic networks

Two source-sink (directed) networks are called path-isomorphic if there exists a bijection π between their arc sets that preserves (simple) source-sink directed paths. Although path-isomorphic networks need not be isomorphic (they need not even have the same number of nodes), we show that several properties are preserved. For example, suppose N and N′ are path-isomorphic. Then, N is acyclic if and only if N′ is acyclic. B is the arc set of block of N if and only if π(B) is the arc set of a block of N′. Also, D is the arc set of a dicomponent of N if and only if π(D) is the arc set of a dicomponent of N′. In addition, we prove a dipath version of Whitney's well-known 2-isomorphism theorem for a special class of networks, which includes the acyclic networks.     

Competing trade mechanisms and monotone mechanism choice

We investigate the choice between posted prices and auctions of competing sellers with private valuations. Assuming that buyers face higher hassle costs in auctions, we show the existence of monotone pure strategy equilibria where sellers offer posted prices rather than auctions if and only if they have a sufficiently high reservation value. Posted prices sell with lower probability but yield a larger revenue in case of trade. Using an empirical strategy to compare revenues of posted prices and auctions that takes selling probabilities explicitly into account, we find our theoretical predictions supported by data from eBay auctions on ticket sales for the EURO 2008 European Football Championship.     

A Hamilton-Jacobi-Bellman approach to optimal trade execution

The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a linear-quadratic (LQ) optimal stochastic control problem. A semi-Lagrangian scheme is used to solve the resulting nonlinear Hamilton-Jacobi-Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparison property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.