A note on the equilibrium theory of economies with asymmetric information

In this note, we give an equilibrium existence theorem for exchange economies with asymmetric information and with an infinite dimensional commodity space. In our model, we assume that preferences are represented by well behaved utility functions, the positive cone has a non empty interior and the individual rational utility set is compact. Our result complements the corresponding one in Podczeck and Yannelis (2008), in the sense that is applicable to commodity spaces in which the order intervals are (possibly) not compact with respect to any Hausdorff linear topology.     

A PRIMER ON MATHEMATICAL MODELLING IN ECONOMICS

Abstract The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics ( Krueger, 1991 ; Colander, 1998, 2005 ). This paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists. In the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of Arrow's impossibility theorem. Common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students, teachers and researchers specializing in different sub‐fields of economics.     

On Social Statement Spaces

In this fundamental draft we shall introduce the concept of social propositional spaces as a general notion of social science and in particular language, logic and methodology. This should help us bridge an old gap between extension and cognition, or said in more specific words, between space as conceived in mathematics or physics and space as is brought in by social location, by the meaning of predicates, their explanation and logic. ¹ We shall not rely on the idea of factor analysis where some “main components” are fit into the data. Because the notion of euclidean normalization and orthogonality, in this context, is a bit artificial. We first show how combinatorial manifolds of statements can be represented in finite vector spaces over the Galois field F₂. This space which we denote as logic statement space can be spanned by generators of alternating codes. In this way the old concepts of truth tables and interaction attributes can be linked to informatics and in particular code theory and geometry. Extending the logic statement space onto a real vector space by mapping units of the finite rings onto units of the real rings we obtain logistic statement spaces. It turns out that vectors in logistic statement spaces represent cross-tables of logits connected with logistic regression analysis. As a completion of the theory we show that the logit is the first derivative of entropy with respect to probability.     

大城市地下空间利用及前景分析——以广州市为例

在快速城市化的现实态势下,大城市对地下空间存在多方面的需求.首先,地下空间对大城市的发展具有安全意义.其次,地下空间可为大城市提供进一步发展的空间.另外,地下空间可为完善大城市的综合功能提供条件.分析了广州市地下空间开发利用现状和存在的问题,在此基础上提出解决问题的对策,并结合发达国家的相关理论和经验进一步阐述了地下空间开发利用的前景.     

Non-cooperative games on hyperfinite Loeb spaces

We present a particular class of measure spaces, hyperfinite Loeb spaces, as a model of situations where individual players are strategically negligible, as in large non-anonymous games, or where information is diffused, as in games with imperfect information. We present results on the existence of Nash equilibria in both kinds of games. Our results cover the case when the action sets are taken to be the unit interval, results now known to be false when they are based on more familiar measure spaces such as the Lebesgue unit interval. We also emphasize three criteria for the modelling of such game-theoretic situations—asymptotic implementability, homogeneity and measurability—and argue for games on hyperfinite Loeb spaces on the basis of these criteria. In particular, we show through explicit examples that a sequence of finite games with an increasing number of players or sample points cannot always be represented by a limit game on a Lebesgue space, and even when it can be so represented, the limit of an existing approximate equilibrium may disappear in the limit game. Thus, games on hyperfinite Loeb spaces constitute the ‘right' model even if one is primarily interested in capturing the asymptotic nature of large but finite game-theoretic phenomena.     

Salmon's critique of Hempel: an alternative view of statistical explanation and theory building

This paper outlines and discusses Wesley Salmon's S-R model of explanation, and commends it to the favorable attention of political scientists. The discussion undertaken here proceeds in three general sections. The first recounts Hempel's account of deductive-nomological (D-N) and inductive-statistical (I-S) explanation. The discussion will particularly note those aspects of Hempel's account that impart special stringency to the requirements of I-S explanation. Section Two unfolds Salmon's S-R model of explanation, which is both a positive account of his model and a critique of the Hempelian account. The third section illuminates those aspects of Salmon's account that make it particularly useful to researchers who are attempting to develop and test theories en route to explanation. The paper concludes with some comments about the usefulness to political scientists of Salmon's S-R model.     

The joint continuity of the expected payoff functions

Glicksberg [Glicksberg, I.L., 1952. A further generalization of the Kakutani fixed point theorem, with applications to Nash equilibrium points. In: Proceedings of the American Mathematical Society 3, pp. 170–174] generalized the Kakutani fixed point theorem to the setting of locally convex spaces and used it to prove that every k-person strategic game with action sets convex compact subsets of locally convex spaces and continuous payoff functions has a Nash equilibrium. He subsequently used this result to establish the following fundamental theorem of game theory: Every k-person strategic game with action sets metrizable compact topological spaces and continuous payoff functions has a mixed strategies equilibrium. However, in his proof of the latter result, Glicksberg did not show that the expected payoff functions were jointly continuous, something that was required for the existence of a mixed strategies equilibrium.     

Innovation ecosystems as a service: Exploring the dynamics between corporates & start-ups in the context of a corporate coworking space

The desire to create innovative organizational spaces has led to various instantiations of innovation ecosystems. Towards this direction, there is a growing interest in establishing corporate innovation ecosystems in the form of ‘corporate coworking spaces’ (CWS). From a relational ontological standpoint, this study builds on the collaborative spaces literature with the aim to investigate the emerging dynamics between corporates and start-ups in an innovation ecosystem. Through an abductive research strategy (ARS) as well as service design methods, we explore how co-creation between corporates and start-ups emerges (or not) in an innovation ecosystem that serves as a collaborative space in Denmark. Our empirical findings challenge the mostly overenthusiastic connotations and thus the study contributes to the critical coworking research stream. More specifically, we give emphasis on the co-constructive entanglement of socio-spatial arrangements and we propose a framework for revisiting the design of CWS through 1) balancing the engineered and evolving parts of the ecosystem, 2) facilitating stakeholder alignment, 3) adopting a service-oriented approach and 4) developing inclusive strategies. Apart from the implications for scholars and practitioners who study and design CWS, we argue that future research would especially benefit from building on a service-oriented approach of innovation ecosystems and we call for more interdisciplinary research.     

Development Regimes,Scales and State Spatial Restructuring: Change and Continuity in the Production of Urban Space in Metropolitan Rio de Janeiro,Brazil

Using the experience of metropolitan Rio de Janeiro, this article contributes to the broader debate on development regimes, rescaling and state spatial restructuring in Brazil, and its specificities in relation to the international discussion on the transformations in Atlantic Fordism. I argue that the transition from a (peripheral) development state to a competitive and rescaled regime has been accompanied by important continuities. Legitimized through discourses around development poles and trickle‐down effects, the national‐developmental regime has systematically promoted some spaces as opposed to others, without much emphasis on the social and environmental dimensions of spatial policies. The emerging competitive state spatial regime, whether in its neoliberalized, or its more recent ‘rolled‐out’ national‐developmental version, is merely expected to aggravate the historical socio‐environmental contradictions in the production of space. Moreover, scale has proven contested and strategic‐relational, both molding and being influenced by actors that seek to use scalar politics to reach their interests. My analysis suggests that, within this scenario, neither economic growth, nor regulatory and institutional strengthening, nor financial resources are likely to produce structural transformation in the inherited spaces of Greater Rio de Janeiro.     

Probability theory in fuzzy sample spaces

This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of The investigations are focussed on the discussion how to equip those sample spaces with suitable -algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature.Acknowledgement. The author would like to thank the participants of the 23rd Linz Seminar on Fuzzy Set Theory for the intensive discussion of the paper. Especially he is indebted to Professors Diamond and Höhle whose remarks have helped to get deeper insights into the subject. Additionally, the author is grateful to one anonymous referee for careful reading and valuable proposals which have led to an improvement of the first draft.This paper was presented at the 23rd Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 5–9, 2002.     

Translating Space: the Politics of Ruins,the Remote and Peripheral Places

This essay surveys recent artistic, literary and philosophical treatments of landscape that use metaphors of ruination, remoteness and the periphery. The discussion primarily focuses on Patrick Keiller's recent works, particularly his film Robinson in Ruins, the account of remote spaces in Paul Farley and Michael Symmons Roberts' book Edgelands, and a collection of essays by Stavros Stavrides on peripheral urban spaces, Towards the City of Thresholds. These treatments of landscape offer an attention to the social significance of spaces overlooked within wider cultural representations of place. It is suggested that all three illustrate the argument that mundane spaces can be read and translated into politicized landscapes offering alternative readings of past events, as well as potential directions for future forms of sociality.     

传统四合院民居建筑的灰空间构成探析

四合院布局的传统民居包含着不同的功能空间,灰空间是内部空间和外部空间的衔接和过渡。文章选取了四合院民居建筑中具有代表性的灰空间部位进行研究,不仅为人们深入认识中国传统四合院的空间构成提供新的视点,同时也希望此文为现代建筑空间的设计起到一定的启示。     

A Note on Seasonal Unit Root Tests

The seasonal unit root tests make it possible to determine the nature of the deterministic and stochastic seasonal fluctuations. In Section 2, we define the main seasonal time series models and the seasonal integration notion. Section 3 describes the HEGY test procedure.     

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.     

Human Resourcing in Practice: Managing Employment Issues in the University

Participant observation in two universities is used to throw light on processes of sensemaking engaged in by managers concerned with human resourcing issues. Analysis of managerial sensemaking in the case study organizations is carried out using concepts from earlier sociological theorizing about human resource or personnel management, treating these theoretical ideas as resources for use in the researchers' own sensemaking. It is shown that theoretical 'sense' can be made of the managerial or 'lay' sensemaking in the universities in terms of a need to handle various tensions which are inherent in all employment management work in industrial capitalist societies. And it is argued that there is clear continuity between what is currently occurring and has occurred in the past. This interpretation is shown to differ from that of an alternative approach in social science sensemaking, that which uses the notion of a new paradigm of 'HRM'.     

Towards a spatial perspective: An integrative review of research on organisational space

Although the notion of space has gained considerable attention in organisation studies, it remains vague, and the respective literature is fragmented. In this paper, we review the empirical literature on organisational space with the aim of synthesising the findings of existing research and thereby facilitating the development of cumulative knowledge in this field. We highlight three dominant concepts that define space: boundaries, distance and movement. Furthermore, we identify four major spatial themes: the distribution of positions in space, the isolation of space, the differentiation of spaces and the intersection of distinct spaces. On that basis, we develop a comprehensive research framework and propose an agenda for future research on organisations from a spatial perspective.     

Wavelet thresholding for some classes of non–Gaussian noise

Wavelet shrinkage and thresholding methods constitute a powerful way to carry out signal denoising, especially when the underlying signal has a sparse wavelet representation. They are computationally fast, and automatically adapt to the smoothness of the signal to be estimated. Nearly minimax properties for simple threshold estimators over a large class of function spaces and for a wide range of loss functions were established in a series of papers by Donoho and Johnstone. The notion behind these wavelet methods is that the unknown function is well approximated by a function with a relatively small proportion of nonzero wavelet coefficients. In this paper, we propose a framework in which this notion of sparseness can be naturally expressed by a Bayesian model for the wavelet coefficients of the underlying signal. Our Bayesian formulation is grounded on the empirical observation that the wavelet coefficients can be summarized adequately by exponential power prior distributions and allows us to establish close connections between wavelet thresholding techniques and Maximum A Posteriori estimation for two classes of noise distributions including heavy–tailed noises. We prove that a great variety of thresholding rules are derived from these MAP criteria. Simulation examples are presented to substantiate the proposed approach.     

Commitment: A mathematical model

The concept of commitment has received ever-increasing attention from social scientists during the past fifteen years. Its usage occurs in several seemingly disjoint problem areas, but it is typically introduced when available explanations fail to describe the tendency for individuals to persist on a given course of action, once started, without obvious motive for doing so. Until recently its theoretical status has been as a primitive term, often appearing in ad hoc explanations, and accepted without question. In sociology, the first major query into the nature of commitment was Howard Becker's “Notes on the Concept of Commitment” (1960), a particularly influential article in stimulating research on commitment. However, most subsequent empirical work has dealt with the correlates and effects of commitment rather than with its genesis. Regrettably, what was once a problem in ad hoc theorizing has come to be matched by ad hoc operationalization of the concept. The present paper is a response to a perceived need for a formal model of commitment whose features might make the concept amenable to uniform theoretical and empirical usage. The purpose of this paper is to present a mathematical model of a general commitment mechanism which complements some extant ideas about the formal role of commitment in explaining certain types of behavior. The first part of the paper concentrates on extracting ideas from sociological and social psychological literature which provide the foundation for the intuitions to be formalized later. The second part presents a mathematical model of commitment. The third part discusses commitment in the context of a turnover model, and in concluding suggests some possible revisions and extensions of the model.     

Pure and randomized equilibria in the stochastic von Neumann–Gale model

The paper examines the problem of the existence of equilibrium for the stochastic analogue of the von Neumann–Gale model of economic growth. The mathematical framework of the model is a theory of set-valued random dynamical systems defined by positive stochastic operators with certain properties of convexity and homogeneity. Existence theorems for equilibria in such systems may be regarded as generalizations of the Perron–Frobenius theorem on eigenvalues and eigenvectors of positive matrices. The known results of this kind are obtained under rather restrictive assumptions. We show that these assumptions can be substantially relaxed if one allows for randomization. The main result of the paper is an existence theorem for randomized equilibria. Some special cases (models defined by positive matrices) are considered in which the existence of pure equilibria can be established.