Unilateral vs. bilateral link-formation: A transition without decay

We provide a model that bridges the gap between the simplest variation of two benchmark models of strategic network formation: Bala and Goyal’s two-way flow model without decay, where links can be unilaterally formed, and a variation of Jackson and Wolinsky’s model based on bilateral formation of links assuming no decay. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the flow through the link suffers some degree of decay, but when it is supported by both the flow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have a simple variation of Jackson and Wolinsky’s connections model assuming no decay, while when flow in those links is perfect we have Bala and Goyal’s two-way flow model without decay. We study Nash, strict Nash and pairwise Nash stability for the intermediate models. Efficiency and dynamics are also examined.     

Asymmetric flow networks

This paper provides a new model of network formation that bridges the gap between the two benchmark game-theoretic models by Bala and Goyal (2000a) – the one-way flow model, and the two-way flow model – and includes both as limiting cases. As in both the said models, a link can be initiated unilaterally by any player with any other in what we call an “asymmetric flow” network, and the flow through a link towards the player who supports it is perfect. Unlike those models, there is friction or decay in the opposite direction. When this decay is complete there is no flow and this corresponds to the one-way flow model. The limit case when the decay in the opposite direction (and asymmetry) disappears corresponds to the two-way flow model. We characterize stable and strictly stable architectures for the whole range of parameters of this “intermediate” and more general model. A study of the efficiency of these architectures shows that in general stability and efficiency do not go together. We also prove the convergence of Bala and Goyal’s dynamic model in this context.     

个体异质对纳什网络存在性的影响研究(英文)

在Bala and Goyal(2000)提出的双向流网络形成模型基础上,研究当个体存在异质性时对纳什网络存在性的影响.分别针对几种不同的环境设定下的个体异质性进行研究,发现个体的连接成本异质性是决定纳什网络存在性的重要因素;但相较于个体的连接成本而言,连接价值的异质性对纳什网络存在性的影响不大.     

Strict Nash networks and partner heterogeneity

This paper extends the two-way flow model of network formation initiated by Bala and Goyal (Econometrica 68(5):1181–1230, 2000) by allowing for partner heterogeneity. In our model if a player i forms a link with player j, then she pays a cost of c _j and gets benefits of V _j . Our main result consists of the characterization of strict Nash networks. We find that the introduction of partner heterogeneity plays a major role in dramatically increasing the set of strict Nash equilibria. This result differs substantially from what Galeotti et al. (Games Econ Behav 54(2):353–372, 2006) find in the two-way flow connections model of network formation with player heterogeneity.     

Network formation under mutual consent and costly communication

We consider two different approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider a network-based approach; in particular Jackson–Wolinsky’s concept of pairwise stability. Next, we discuss a non-cooperative game-theoretic approach, through a refinement of the Nash equilibria of Myerson’s consent game. This refinement, denoted as monadic stability, describes myopically forward looking behavior of the players. We show through an equivalence that the class of monadically stable networks is a strict subset of the class of pairwise stable networks that can be characterized fully by modifications of the properties defining pairwise stability.     

Equilibrium selection and altruistic behavior in noncooperative social networks

Given their importance in determining the outcome of many economic interactions, different models have been proposed to determine how social networks form and which structures are stable. In Bala and Goyal (Econometrica 68, 1181–1229, 2000), the one-sided link formation model has been considered, which is based on a noncooperative game of network formation. They found that the empty networks, the wheel in the one-way flow of benefits case and the center-sponsored star in the two-way flow case play a fundamental role since they are strict Nash equilibria of the corresponding games for a certain class of payoff functions. In this paper, we first prove that all these network structures are in weakly dominated strategies whenever there are no strict Nash equilibria. Then, we exhibit a more accurate selection device between these network architectures by considering “altruistic behavior” refinements. Such refinements that we investigate here in the framework of finite strategy sets games have been introduced by the authors in previous papers.     

动态经济网络结构及其稳定性研究

在Jackson和Wolinsk71996年提出的经济网络的内生形成模型的基础上,进行模型的动态扩展研究．探讨在网络中随时间序列的变化,每个时间步内都有一个新节点增加的动态变化状态下,模型构成的变化情况．随着网络的动态变化,模型的稳定性和静态网络中的稳定性是不同的,因此也探讨了在动态模型中动态稳定性的含义,并给出了不同约束条件下,形成的动态稳定网络结构及其有效性的初步探讨．     

A Shapley value representation of network potentials

We consider network formation games by Jackson and Wolinsky (J Econ Theory 71:44–74, 1996) and characterize the class of games that have a network potential. We show that there exists a network potential if and only if each player’s payoff function can be represented as the Shapley value of a special class of cooperative games indexed by the networks. We also show that a network potential coincides with a potential of the same class of cooperative games.     

Unequal connections

Empirical work suggests that social and economic networks are characterized by an unequal distribution of connections across individuals. This paper explores the circumstances under which networks will or will not exhibit inequality. Two specific models of network formation are explored. The first is a playing the field game in which the aggregate payoffs of an individual depend only on the number of his links and the aggregate number of links of the rest of the population. The second is a local spillovers game in which the aggregate payoffs of an individual depend on the distribution of links of all players and the identity of neighbors. For both class of games we develop results on existence and characterize equilibrium networks under different combinations of externalities/spillovers. We also examine conditions under which having more connections implies a higher payoff.     

One-way flow network formation under constraints

We study the effects of institutional constraints on stability and efficiency in the “one-way flow” model of network formation. In this model the information that flows through a link between two players runs only towards the player that initiates and supports the link, so in order for it to flow in both directions, both players must pay whatever the unit cost of a directional link is. We assume that an exogenous “societal cover” consisting of a collection of possibly overlapping subsets covering the set of players specifies the social organization in different groups or “societies,” so that a player may initiate links only with players that belong to at least one society that he/she also belongs to, thus restricting the feasible strategies and networks. In this setting, we examine the impact of such societal constraints on stable/efficient architectures and on dynamics.     

Critical agents in networks

We examine the fundamental tension between efficiency and stability in social network formation. Jackson and Wolinsky (JET, 1996) showed that the component-wise egalitarian payoff rule supports an efficient network as being pairwise stable if and only if the network benefit function is critical link monotone. We extend this insight to strong pairwise stability and derive that the critical link monotonicity condition has to be strengthened to a condition on individuals occupying critical positions in the network.     

带上下界的双参与人双向委托代理模型及优化算法研究

考虑现实中双参与人同时具有委托人和代理人双重身份情形下,双参与人间的互为委托代理关系,设计虚拟委托人期望效用函数表达式,建立带上下界的双参与人双边约束双向委托代理模型,利用不动点定理确定参数的上下界,并运用不等式组的旋转算法并结合序列二次规划算法进行求解.通过算例分析表明,为达到联盟总效用最大化,需通过确定联盟成员各自合适的保留效用值,以平衡联盟成员的投资和回报,真正实现对联盟成员的激励.     

内生网络环境下具有异质连接费用的局部策略互动

考察内生网络环境下局中人之间的局部策略互动, 网络中的局中人只与直接邻居进行协同对策. 网络生成的过程中, 建立连接的费用是异质的~(具有两种水平), 与采取有效行动的局中人建立连接时执行高水平费用, 与采取风险占优行动的局中人建立连接时执行低水平费用. 在异质连接费用的情形下, 首次较为完整地给出了均衡网络的结构特性和局中人的行动选择, 并分析了费用参数对均衡结果的影响.     

超网络博弈的位置值的公理化刻画

在图博弈中,Myerson假设只有连通的联盟才能获得完全的效用,而忽略连通联盟的具体结构.1996年,Jackson和Wolinsky提出了“网络情形博弈”的模型,拓展了Myerson的图博弈模型.它是利用值函数代替原来的特征函数以体现不同网络结构对合作结果的影响.考虑超网络情形博弈,它是网络情形博弈的自然推广,由三元组（N,H,v）所组成,这里v是值函数,用于描述在超网络（N,H）合作结构下的合作收益.2012年,van den Nouweland和Slikker利用四个公理给出了位置值的公理化刻画.通过分支有效性和局部平衡超边贡献性两个公理,给出了超网络博弈中位置值的公理化刻画.作为推论,得到了网络博弈中位置值的新刻画.     

Network formation when players seek confirmation of information

We study network formation in a situation where the network allows players to obtain information (signals) about other players. This information is important for making a payoff relevant decision. However, not all information is reliable and so players may have an incentive to check it. By obtaining multiple messages about the same player through the network, a player learns whether his information is reliable for making the payoff relevant decision. We study the existence and architecture of strict Nash networks. We find that players who are involved in at least three links sponsor all links they are involved in. These players are similar to the central players in center sponsored stars. We show that strict Nash networks can be over-connected as well as under-connected as compared to efficient networks. Finally, we extend the basic model to study heterogeneous populations. In the first scenario, we allow for the co-existence of players who only value checked information and players who also value information with unknown reliability. In the second scenario, players who do not care about checking their information co-exist with players who do. Our results are robust to both types of heterogeneity, with one exception: the presence of a single player who cares only about checked information is enough to ensure that center sponsored stars are no longer stable.     

于改进UGF算法的线性拓扑WSN系统可靠性评估

提出了面向感知数据融合的通用发生函数(UGF)改进算法,并使用该算法对线性拓扑结构的无线传感网络(WSN)可靠性进行了评估。首先对PEGASIS协议下WSN的线性拓扑结构及数据传输过程进行抽象,建立了双向连续k/n:F系统模型。然后根据WSN感知数据传输及融合方式,在改进算法中重新定义了传感节点的UGF表达式和组合算子。最后对双向连续k/n:F模型进行单向化分解,根据得到的单向模型可靠性推导出双向模型的可靠性表达式。通过具体实例对提出的改进算法进行了验证,计算结果显示改进的算法可有效解决传感网络线性拓扑结构可靠性评估问题。     

Students’ conceptualisations of multiplication as repeated addition or equal groups in relation to multi-digit and decimal numbers

Multiplicative understanding is essential for mathematics learning and is supported by models for multiplication, such as equal groups and rectangular area, different calculations and arithmetical properties, such as distributivity. We investigated two students’ multiplicative understanding through their connections between models for multiplication, calculations and arithmetical properties and how their connections changed during the school years when multiplication is extended to multi-digits and decimal numbers. The case studies were conducted by individual interviews over five semesters. The students did not connect calculations to models for multiplication, but showed a robust conceptualisation of multiplication as repeated addition or equal groups. This supported their utilisation of distributivity to multi-digits, but constrained their utilisation of commutativity and for one student to make sense of decimal multiplication     

A bargaining approach to coordination in networks

This paper, presents a model in which players interact via the formation of costly links and the benefits of bilateral interactions are determined by a stag-hunt game. A novel contribution of this paper is that the fraction of the cost borne by each player involved in a bilateral link is not fixed exogenously, but results from bargaining. We analyze the model both in a static and a dynamic setting. Whereas the static game has multiplicity of equilibria, we show that only one is stochastically stable. This is a revised version of Chapter 1 of my Ph.D. Thesis presented at Universidad de Alicante. A previous version of this paper circulated with the title “Network Formation and Coordination: Bargaining the Division of Link Costs” (IVIE WP-AD 2002-27). I am indebted to Fernando Vega-Redondo for many helpful conversations, suggestions and encouragement. I am grateful to Julio González-Díaz, Antonio J. Morales, Ascensión Andina-Díaz and the Associate Editor for valuable suggestions. I also thank Jordi Brandts, Antonio Cabrales, Angel Hernando, Andrea Galeotti, Sanjeev Goyal, Christoph Kuzmics, Ana Lozano-Vivas, Paola Manzini, Juan Mora, Efe Ok, Juana Santamaría-García and José A. Silva for their comments. I gratefully acknowledge the hospitality of New York University, where part of this research was carried out, and the financial support from the Spanish Ministry of Education (ref. BEC2002-02852).     

Inventory models for perishable items with inventory level dependent demand rate

This paper presents inventory models for perishable items with inventory level dependent demand rate. The models with and without backlogging are studied. In the backlogging model, it is assumed that the backlogging rate is dependent on the waiting time and the amount of products already backlogged simultaneously. Two cases that holding inventory is profitable or not are studied, respectively. The smallest shelf space to ensure shortage not occur when holding inventory is not profitable is obtained. In the model without backlogging, it is assumed that the remaining stock at the end of the inventory cycle is disposed of with salvage value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution of these models are investigated. At last, some numerical examples are presented to illustrate the effectiveness of the proposed model. The model in this paper is generalization of present ones. In particularly, the model is reduced to Padmanabhan and Vrat’s when δ₁ = 0, and Dye and Ouyang’s when δ₂ = 0. If S = s and δ₂ = 0, it is Chang, Goyal and Teng’s model.     

A network traffic flow model for motorway and urban highways

The research reported in this paper develops a network-level traffic flow model (NTFM) that is applicable for both motorways and urban roads. It forecasts the traffic flow rates, queue propagation at the junctions and travel delays through the network. NTFM uses sub-models associated with all road and junction types that comprise the highway. The flow at any one part of the network is obviously very dependent on the flows at all other parts of the network. To predict the two-way traffic flow in NTFM, an iterative simulation method is executed to generate the evolution of dependent traffic flows and queues. To demonstrate the capability of the model, it is applied to a small case study network and a local Loughborough–Nottingham highway network. The results indicate that NTFM is capable of identifying the relationship between traffic flows and capturing traffic phenomena such as queue dynamics. By introducing a reduced flow rate on links of the network, the effects of strategies used to carry out roadworks can be mimicked.