A note on the space of preference relations

The space of irreflexive, transitive, and continuous binary relations of R^l endowed with the topology of closed convergence, and subsets of defined by various other properties of the relations are investigated. It is shown that the subsets defined by properties, which one often assumes in general equilibrium theory, have nice topological properties such as compactness or G₈-ness.     

The non-existence of a universal topological type space

The concept of types was introduced by Harsányi (1967–1968). In the literature there are two approaches for formalizing types, type spaces: the purely measurable and the topological models. In the former framework Heifetz and Samet (1998) showed that the universal type space exists and later Meier (2001) proved that it is complete. In this paper we examine the topological approach and conclude that there is no universal topological type space in the category of topological type spaces.     

The international-trade network: gravity equations and topological properties

This paper begins to explore the determinants of the topological properties of the international-trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a “residual” ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and so on. We then compare the topological properties of the original and residual ITNs. We find that the residual ITN displays, unlike the original one, marked signatures of a complex system, and is characterized by a very different topological architecture. Whereas the original ITN is geographically clustered and organized around a few large-sized hubs, the residual ITN displays many small-sized but trade-oriented countries that, independently of their geographical position, either play the role of local hubs or attract large and rich countries in relatively complex trade-interaction patterns.     

Topological properties of reconstructed credit networks and banking systemic risk

Financial bipartite networks provide channels for contagion risks and their topological properties determine financial stability. We enrich the bipartite network reconstruction methods proposed by Ramadiah et al. (2020) and extend them to the Chinese banking system. By comparing the reproducibility of the real credit market and the corresponding systemic risk, the impact of topological properties for different reconstructed bipartite networks on financial stability is analyzed. The empirical evidence shows that network reconstruction methods based on maximum entropy ensembles capture more properties in the real credit network. It also highlights that the different systemic risk level is mainly contributed by the topological properties based on common exposures. These analyses for topological properties provide regulatory insights for systemic risk prevention. It shows that reducing credit similarity across banks while increasing credit diversification in different sectors helps to control systemic risk. The results imply the possibility of increasing financial stability through the macro-regulation of the credit market structure.     

A topological approach to Wilson’s impossibility theorem

We will present a topological approach to Wilson’s impossibility theorem [Wilson, R.B., 1972. Social choice theory without the Pareto principle. Journal of Economic Theory 5, 478–486] that there exists no non-null binary social choice rule which satisfies transitivity, independence of irrelevant alternatives, non-imposition and has no dictator nor inverse dictator. Our research is in line with the studies of topological approaches to discrete social choice problems initiated by [Baryshnikov, Y., 1993. Unifying impossibility theorems: a topological approach. Advances in Applied Mathematics 14, 404–415]. This paper extends the result about the Arrow impossibility theorem shown in [Tanaka, Y., 2006. A topological approach to the Arrow impossibility theorem when individual preferences are weak orders. Applied Mathematics and Computation 174, 961–981] to Wilson’s theorem.     

一类树的Hosoya指标序列

许多拓扑指标都与分子的某些物理化学性质密切相关,而不同的分子拓扑指标反映该分子的不同性能。其中Hosoya指标是较为重要的拓扑指标之一。设G一个分子结构图模型,即为一个具有n个顶点的连通图,则图G的Hosoya指标Z(G),是指这样一些子集的个数,每一个子集中的任意两条边在图G中都没有公共的顶点,即图G中匹配的个数,包括空集。本文讨论了一类四叶树的Hosoya指标序列。     

Competitive equilibria in general choice spaces

This paper primarily demonstrates the existence of Arrow-Debreu equilibria in a general class of topological vector spaces of commodity bundles. Two conditions based on production possibilities, preferences, and the topological nature of bounded sets are shown to substitute, in any locally convex space, for the advantages of the Euclidean topology. Examples fulfilling these conditions are supplied. The approach is that of Bewley, demonstrating equilibria on finite dimensional sub-economies and establishing a net of these equilibria that converges to an equilibrium on the whole commodity space. An example of equilibrium with a storage technology is given. An auxiliary result concerns the price support of efficient allocations.     

基于拓扑势的军事物流网络效能度量模型研究

运用拓扑势建立了军事物流网络效能度量模型,真实表现了各个节点和网络整体效能分布数据场。最后通过战区军事物流网络拓扑结构分析和效能度量实例,表明了此方法的科学性和有效性。     

General conditions for the existence of maximal elements via the uncovered set

This paper disentangles the topological assumptions of classical results (e.g.,Walker, 1977 on the existence of maximal elements from rationality conditions. It is known from the social choice literature that under the standard topological conditions—with no rationality assumptions on preferences—there is an element such that the upper section of strict preference at that element is minimal in terms of set inclusion, i.e., the uncovered set is nonempty. Assuming the finite subordination property, a condition that weakens known acyclicity and convexity assumptions, each such uncovered alternative is in fact maximal. Implications are a generalization of a result of Yannelis and Prabhakar (1983) on semi-convexity, an extension of Fan’s (1961) lemma on KKM correspondences, and the existence of fixed points for subordinate convex correspondences generalizing the work of Browder (1968).     

Modeling the International-Trade Network: a gravity approach

We investigate whether the gravity model (GM) can explain the statistical properties of the International Trade Network (ITN). We fit data on trade flows with a GM using alternative estimation techniques and we build GM-based predictions for the weighted topological properties of the ITN, which are then compared to the observed ones. Our exercises show that the GM: (i) may replicate part of the weighted-network structure only if the observed binary architecture is kept fixed; (ii) is not able to explain higher-order statistics that, like clustering, require the knowledge of triadic link-weight topological patterns, even if the binary structure perfectly replicates the observed one; (iii) performs very badly when asked to predict the presence of a link, or the level of the trade flow it carries, whenever the binary structure must be simultaneously estimated.     

A functional perspective on financial networks

The financial sector is a critical component of any economic system, as it delivers key qualitative asset transformation services in terms of liquidity, maturity and volume. Although these functions could in principle be carried out separately by specialized actors, in the end it is their systemic co-evolution that determines how the aggregate economy performs and withstands disruptions. In this paper we argue that a functional perspective on financial intermediation can be usefully employed to investigate the functioning of financial networks. We do this in two steps. First, we use previously unreleased data to show that focusing on the economic functions performed over time by the different institutions exchanging funds in an interbank market can be informative, even if the underlying topological structure of their relations remains constant. Second, a set of alternative artificial histories are generated and stress-tested by using real data as a calibration base, with the aim of performing counterfactual welfare comparisons among different topological structures.     

A remark on topological robustness to bounded rationality in semialgebraic models

In this short note, we show that the compact semialgebraic class of Anderlini and Canning (2001) is topologically robust, i.e. the topological properties of the equilibrium set are preserved, deviating parameter values and introducing a small amount of bounded rationality.     

Semicontinuous extension of a partial order

This paper shows that it is always possible to determine an extension of a strict partial order to a strict weak order that preserves simultaneously some order denseness and topological properties; as a corollary, sufficient conditions for the existence of an upper semicontinuous utility on a strictly partially ordered space are derived; a direct proof of a complementary result is also given.     

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces.     

An algebraic index theorem for non-smooth economies

In this paper, we prove an existence theorem for equilibria in production economies with increasing returns, which generalizes the classic results on this topic. In particular, we eliminate both the free-disposal assumptions and any smoothness requirements on the boundary of the production sets. For this purpose, we propose a new definition of the topological degree for non-convex-valued correspondences defined on non-smooth topological manifolds.     

The Only Way Is Up? Ordinary Topologies of Ramallah

This article seeks to conceptualize and value some of the quotidian geographies responsible for contemporary forms of urban change. The starting point for the argument is an attempt to account for recent urban change in the Palestinian city of Ramallah, particularly the proliferation of apartment buildings, using emerging work on verticality. It is argued that work on verticality focuses empirically on prominent cities and spaces of violent conflict, invokes the vertical as politically suspect and offers a theorization of space that is topographical in nature. Consequently, accounts of verticality have produced narratives that obscure topological spatial relations. This article seeks to make space for such topologies, which it is argued are crucial to producing urban and political life itself in many contexts. The concept of ordinary topologies is proposed as a means of attending to the complex and undervalued practices that are thought to be normal (but not static) and common within and across intensive or qualitative spatio‐temporal relations. This approach is fleshed out through a discussion of changing topographic–topological landscapes in Ramallah. In particular, it is argued that the increasingly verticalized landscape of the city, embodied in rapidly proliferating apartment buildings, must be understood in relation to frequent journeys to other places and changing family relations.     

网络结点拓扑编号及程序设计

采用结点拓扑编号方法将原有不规则的网络结点编号，调整为正确、合理的新结点编号。阐述结点拓扑编号方法过程，也列举了具体实例，并用BASIC语言编程。     

The topological equivalence of the pareto condition and the existence of a dictator

The paper studies two standard properties of rules for aggregating individual into social preferences: non-dictatorship and the Pareto condition. Together with the condition of independence of irrelevant alternatives, these are the three basic axioms of Arrow's social choice paradox.We prove the topological equivalence between the Pareto condition and the existence of a dictator for continuous rules. The axiom of independence of irrelevant alternatives is not required.The results use a topological framework for aggregation introduced in Chichilnisky (1980), but under different conditions. In Chichilnisky (1980) rules are anonymous and respect unanimity. Since anonymity is strictly stronger than the condition of non-dictatorship, while respect of unanimity is strictly weaker than the Pareto condition, the two sets of conditions are not comparable.     

Ramsey policies in a small open economy with sticky prices and capital

This paper analyzes jointly optimal fiscal and monetary policies in a small open economy with capital and sticky prices. We allow for trade in consumption goods under perfect international risk-sharing. We consider balanced-budget fiscal policies where authorities use distortionary taxes on labor and capital together with monetary policy using the nominal interest rate. First, as long as a symmetric equilibrium is considered, the steady state in an open economy is isomorphic to that of a closed economy. Second, sticky prices’ allocations are almost indistinguishable from flexible prices allocations both in open and closed economies. Third, the open economy dimension delivers results that are qualitatively similar to those of a closed economy but with significant quantitative changes. Tax rates are both more volatile and more persistent to undo the distortions implied by terms of trade fluctuations.