Hierarchies of beliefs for compact possibility models

In this paper, we construct a universal type space for a class of possibility models by imposing topological restrictions on the players’ beliefs. Along the lines of Mertens and Zamir [International Journal of Game Theory, 14 (1985) 1] or Brandenburger and Dekel [Journal of Economic Theory 59 (1993) 189], we show that the space of all hierarchies of compact beliefs that satisfy common knowledge of coherency (types) is canonically homeomorphic to the space of compact beliefs over the state of nature and the types of the other players. The resulting type space is universal, in the sense that any compact and continuous possibility structure can be uniquely represented within it. We show how to extend our construction to conditional systems of compact beliefs.     

城市新商业空间的区位和类型探析

1990年代以来,伴随着快速城市化、城市郊区化及新商业业态的大量出现,新商业空间作为一种新的现象在中国城市中迅速涌现,对传统商业空间和城市整体功能空间结构带来一定影响.新商业空间主要分布在城市核心区、老城区边缘、城郊结合部的快速干道附近和郊区新城,主要包括便利性和日常用品消费空间、选购商品消费空间和高档多功能消费空间等三种主要功能类型.新商业空间的业态、区位及功能类型之间存在一一对应的关系,这个规律可为城市商业网点规划和建设提供相应的理论支撑.     

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.     

A further note on arrow's impossibility theorem

For arbitrary measure spaces of agents we investigate the existence of social welfare functions which fulfill a suitable non-dictatorship axiom; it turns out that there is an essential difference between finite and σ-finite but infinite measure spaces. Furthermore the condition of universal domain of social welfare functions is weakened.     

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.     

The place attachment experience regarding the disabled people: the typology of coffee shops

This study inquires the possible creation of a sense of a place in coffee houses for the disabled people as public places. The physical characteristics of a space are the main factors allowing all people including the disabled ones as well to perceive that place properly and within the “person, place and interaction process” framework. The place attachment, which can be defined as the main emotional bond between space and the users, is heavily influenced by the individualistic experiences and reactions whether they are ordinary or differently abled. In order to initiate a place attachment, spaces should be designed in a way that they respect the occupant’s perception, feelings, memories, senses and their physical abilities to enable them to develop a sense of belonging and ownership. Therefore, creating designs which foster people’s construction process of sense of a place that comprises the concept of identity and sense of belonging, is among the essential issues for realizing place attachment in architecture and design of public spaces. In our contemporary world, there are settings that possess these qualities; contrariwise there are more architectural and urban spaces which ignore these qualities and their benefits for people, especially for the disabled ones. Relatedly, a building should offer people enough information for perceiving it and with its physical features should also support the experiences that occur in it. There is a strong link between memorable events and the space where those events occur. An environment which provides outstanding and meaningful ambiance by its architectural characteristics can establish a sense of a place. Disabled people often have less opportunities to experience the spaces properly compared to others because their limitations are not taken into consideration when designing the public spaces. Therefore, the design process of public spaces should involve the basic needs of disabled people. In order to propose a typology for traditional coffee houses, this research aims to define and discuss the place attachment experience of disabled people in public spaces. The study begins with an overview of identifying different types of disabilities and special needs, and an introductory discussion of how space attachment can help to meet those needs. Therefore, the physical, social and typological aspects of traditional coffee houses were evaluated in terms of location, space organization and functions by considering the profiles of disabled users. Methodologically, this is a case study, which has a mixed research design including qualitative and quantitative research instruments.     

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.     

Nonlinear supporting prices : The superadditive case

Assumptions on allocations and preferences sufficient to allow superadditive price support are considered for an exchange economy with a finite number of traders when the commodity space is an ordered topological vector space. The main requirements are a uniformmonotonicity assumption on preferences and that no permutation of the allocation among agents yields a Pareto improvement. No convexity assumption on preferences is used, the positive orthant need not have interior, while the proof is constructive. Applications to finite and infinite dimensional commodity spaces are discussed.     

Hierarchies of beliefs and the belief-invariant Bayesian solution

The belief-invariant Bayesian solution is a notion of correlated equilibrium in games with incomplete information proposed by Forges (1993), and hierarchy of beliefs over conditional beliefs is introduced by Ely and Peski (2006) in their study of interim independent rationalizability. We study the connection between the two concepts. We partially characterize the correlations embedded among type spaces with the same set of hierarchies of beliefs over conditional beliefs with partially correlating devices, which send correlated signals to players in a way that preserves each player’s belief about others’ types. Since the belief-invariant Bayesian solution is also implemented by such correlating devices, we then establish that it is invariant on equivalent type space.     

Pure strategy equilibria in games with countable actions

In this paper, we extend the Radner–Rosenthal theorem with finite action spaces on the existence of a pure strategy equilibrium for a finite game to the case that the action space is countable and complete. We also prove the existence of a pure strategy equilibrium for a game with a continuum of players of finite types and with a countable and complete action space. To work with the countably infinite action spaces, we prove some regularity properties on the set of distributions induced by the measurable selections of a correspondence with a countable range by using the Bollobás–Varopoulos extension of the marriage lemma.     

An alternative graphical modeling for economics: Econographicology

The rationale of Econographicology revolves around the efficacy of multidimensional graphs as the most effective visual tool to understand any economic phenomenon from a multidimensional view. The main motivation behind the creation of Econographicology is to evaluate multidimensional graphs evolved so far in economics and to develop new type of multidimensional graphs to facilitate the study of economics, as well as finance and business. Thereby, the mission of Econographicology is to offer academics, researchers and policy maker’s an alternative multidimensional graphical modeling approach for the research and teaching–learning process of economics, finance and business from a multidimensional perspective. Hence, this alternative multidimensional graphical modeling approach is offer a set of multi-dimensional coordinate spaces to build different types of multidimensional graphs to study any economic phenomenon. The following new types of multi-dimensional coordinate spaces are presented: the 5-dimensional coordinate space (vertical position and horizontal position), the mega-dynamic disks coordinate space (vertical position and horizontal position), and the mega-disks networks mapping.     

Evaluating spatial service and layout efficiency of municipal Wi-Fi facilities for SmartCity planning: A case study of Wuhan city,China

This paper explores an approach to evaluating spatial service and layout efficiency of municipal Wi-Fi facilities for cyber infrastructure planning in the construction of a smart city. Based on the equilibrium principle that Wi-Fi services supply should meet the spatial demand for recreation, urgency, and security, two evaluation models were built. In the first model, the spatial service efficiency of Wi-Fi facilities is measured by a mean ratio of three types of demand spaces covered by Wi-Fi service. In the other model, spatial layout efficiency of each Wi-Fi facility is calculated by a demand load indicator - the sum of the three types of demand space's ratios of served quantity to the average quantity it should carry, and then assessed by relationship with its adjacent facilities. Corresponding statistical methods and analysis processes were also designed using the function modules found in ArcGIS software. The approach was applied to Wuhan city in 2016. After overlaying influence areas of 688 Wi-Fi facilities with demand spaces of 137 access points for recreation, 1200.99 km roads for urgency, 121.54 km² regions for security, the results show that there exists a spatial disequilibrium between supply and demand of Wi-Fi service in Wuhan due to lack of comprehensive planning. Specifically, there are 67 points, 700.76 km roads, and 42.59 km² regions of demand spaces covered by Wi-Fi service, with service efficiencies of 48.91%, 58.35%, and 35.04% respectively and an overall spatial service efficiency of 47.43%. Among all the Wi-Fi facilities, there are 481 carrying saturated demand, 3 straying from the centre of demand space, and 204 redundant. The overall spatial layout efficiency of Wi-Fi facilities is 43.01%. The conclusion is that the dense and massive redundant Wi-Fi facilities should be optimized, especially in the centre areas along the confluence of Yangtze and Han rivers and new Wi-Fi facilities supplemented in other ill-equipped areas. Since many metropolitan cities experience the same problem, this novel approach will find wide application in the future and offer improved evaluation strategies for researchers and policymakers.     

Homothetic preferences on star-shaped sets

This paper describes properties of homothetic preferences on a subset X of a vector space which is star-shaped with respect to 0 (e.g., a cone). We prove that a preference relation on X is homothetic, greedy and calibrated if and only if there exists a positively homogeneous function that represents it. This function is unique up to a strictly increasing and positively homogeneous transformation. As a corollary, we find that, if X is contained in a topological vector space, then œ is homothetic and continuous if and only if there exists a positively homogeneous and continuous function that represents it.     

Pseudocontinuous functions and existence of Nash equilibria

In topological spaces, we introduce a new class of functions (pseudocontinuous functions) and we present some characterizations and properties. In particular, we show that any preference relation endowed of utility functions is continuous if and only if any utility is pseudocontinuous. A maximum theorem is proved for such a class of functions and connections with similar results are investigated. Finally, the existence of Nash equilibria for games with pseudocontinuous payoffs is obtained.     

Representing complete and incomplete subjective linear preferences on random numbers

We show that preferences on random numbers which satisfy certain natural properties can be represented, in the setting of topological vector spaces, by a suitable family of continuous previsions which is, in a sense, unique. Moreover, for most commonly used spaces of random numbers, we establish that one can derive these preferences, via an expectation operator, from a suitable family of probabilities (whether or not finitely additive). Mathematics Subject Classification (2000): 06A06, 62C05, 91B06 Journal of Economic Literature Classification: D11, D81     

Rationalizability in continuous games

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating “never-best-reply” strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).     

On the impatience implications of Paretian social welfare functions

In this paper, we investigate the impatience implications resulting from the assumption of existence of a Paretian social welfare function (SWF) aggregating infinite utility streams. We show, for very general program spaces, that the set of utility streams, at which the SWF exhibits impatience, has the power of the continuum. In the context of a more special program space, which has figured prominently in the literature, we establish that this set is dense, so that even if there is a point in the program space at which the SWF does not exhibit impatience, there are points close to it at which it does. If the Paretian SWF is continuous (in the sup metric), we show that impatience is generic: the collection of points, at which the SWF does not exhibit impatience, is a closed, nowhere dense set.     

A weak α-core existence theorem of games with nonordered preferences and a continuum of agents

Inspired by Kajii (1992) and Askoura (2011, 2017), we introduce the notion of the weak $\alpha$-core for games with nonordered preferences and a continuum of agents. First, we extend the work of Kajii (1992) to games with spaces of strategies defined on Hausdorff topological vector spaces. Furthermore, we prove the nonemptiness of the weak $\alpha$-core. Finally, we establish the relations between normal-form games, games with nonordered preferences and games with pseudo-utilities.     

基于定量分析的杭州市城市居住空间分异研究

居住空间结构的合理程度,不仅影响城市居民的生活质量,而且影响整个城市效率的实现。居住空间变化的实质是社会结构的变化在居住空间上的表现。本文以问卷调查的方式,收集整理了杭州市内具有一定规模住宅片区的信息资料,运用SPSS统计分析软件对这些住宅片区的信息进行了统计分析及聚类分析,将杭州市居住空间分成主城区老式小区、经济适用房住区、城区中高档小区、新区中高档小区和新区中低档小区等五类。分别阐述了这五类居住空间的分布范围和特点,揭示正在不断演化的城市居住空间分异现象,并归纳总结不同阶层区划化居住的特征,思考城市摆脱居住空间分异负功能的对策。     

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.