Demand functions and reflexivity

In the theory of ordered spaces and in microeconomic theory two important notions, the notion of the base for a cone which is defined by a continuous linear functional and the notion of the budget set are equivalent. In economic theory the maximization of the preference relation of a consumer on any budget set defines the demand correspondence which at any price vector indicates the preferred vectors of goods and this is one of the fundamental notions of this theory. Contrary to the finite-dimensional economies, in the infinite-dimensional ones, the existence of the demand correspondence is not ensured. In this article we show that in reflexive spaces (and in some other classes of Banach spaces), there are only two classes of closed cones, i.e. cones whose any budget set is bounded and cones whose any budget set is unbounded. Based on this dichotomy result, we prove that in the first category of these cones the demand correspondence exists and that it is upper hemicontinuous. We prove also a characterization of reflexive spaces based on the existence of the demand correspondences.     

Implementation by mediated equilibrium

Implementation theory tackles the following problem given a social choice correspondence (SCC), find a decentralized mechanism such that for every constellation of the individuals’ preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under such an equilibrium, the players’ strategies can be coordinated in a way that discourages deviation. Our main result is a complete characterization of SCCs that are implementable by mediated strong equilibrium. This characterization, in addition to being strikingly concise, implies that some important SCCs that are not implementable by strong equilibrium are in fact implementable by mediated strong equilibrium.     

On twice differentiable direct and indirect utility functions and the monotonicity of the demand

This article investigates the relationships between the Hessians of the direct and indirect utility function and the Jacobian of the demand correspondence. The monotonicity of the demand is analysed thanks to the convexity indices of the function and the monotonicity index of the demand.     

一个交换经济核心的极限定理

对极限经济核心的研究是经济研究的一个主要领域,经济学家已经引入了一个强凸偏好假设,确保需求集只包含一个向量.通过采用新的距离概念,本文获得了同样的结果而没有假定强凸偏好--需求集也许包含多个向量.     

The extended serial correspondence on a rich preference domain

We study the problem of assigning objects to a set of agents. We focus on probabilistic solutions that only take agents’ preferences over objects as input. Importantly, agents may be indifferent among several objects. The “extended serial correspondence” is proposed by Katta and Sethuraman (J Econ Theory 131:231–250, 2006) to solve this problem. As a follow-up to Liu and Pycia (Ordinal efficiency, fairness, and incentives in large markets. Mimeo, 2012) who introduce the notion of profiles with “full support”, we work with two interesting classes of preference profiles: profiles that (i) have rich support on a partition or (ii) are single-peaked with rich support on a partition. For each profile in these classes, an assignment matrix is selected by the extended serial correspondence if and only if it is sd-efficient and sd envy-free. We also provide an asymptotic result.     

Preseparable Extensions of Multidimensional Preferences

Throughout much of the literature in economics and political science, the notion of separability provides a mechanism for characterizing interdependence within individual preferences over multiple dimensions. In this paper, we show how preseparable extensions can be used to construct certain classes of separable and non-separable preferences. We prove several associated combinatorial results, and we note a correspondence between separable preference orders, Boolean term orders, and comparative probability relations. We also mention several open questions pertaining to preseparable extensions and separable preferences. This work was partially supported by National Science Foundation grant DMS-0451254, which funds a Research Experience for Undergraduates program at Grand Valley State University. Portions of this paper are adapted from Hodge’s doctoral dissertation [4]. The authors wish to thank the referees and editor for their helpful comments and suggestions.     

消费者非均匀偏好条件下高校项目开发策略

为了探究教育项目消费者随机需求条件下的不同层次高校的竞优策略, 运用Stackelberg博弈方法, 构建了消费者偏好服从非均匀分布的不同层次高校开发同类教育项目的定位设计模型, 分析了消费者偏好行为对教育项目收益的影响规律以及双方的竞优策略。结果显示, H型高校(声誉较高)不受消费者偏好等市场因素影响, 始终选择最大差异化策略。L型高校(声誉较低)在消费者无差异偏好偏向自己一方时也不受市场因素影响采取最大差异化策略; 而在消费者无差异偏好偏向它方时, 若市场需求概率小于0.5则选择最大差异化策略, 否则其决策将受到自身初始位值、市场概率等因素的综合影响, 并适时选择最大差异化、有限差异化或有限趋同化策略。     

On the uniqueness of Bertrand equilibrium

We introduce product differentiation in the model of price competition with strictly convex costs in which firms have to supply all of the forthcoming demand. We find that although a continuum of equilibria exists in a homogeneous product market, the competitive price equilibrium is the only robust one. Specifically, as long as the equilibrium correspondence is nonempty, the equilibrium price converges to the competitive price when the degree of product differentiation shrinks to zero.     

Stochastic optimization on social networks with application to service pricing

In this paper we develop a combined simulation and optimization approach for solving difficult decision problems on complex dynamic networks. For a specific reference problem we consider a telecommunication service provider who offers a telecommunication service to a market with network effects. More particularly, the service consumption of an individual user depends on both idiosyncratic characteristics and the popularity of this service among the customer’s immediate neighborhood. Both the social network and the individual user preferences are largely heterogeneous and changing over time. In addition the service provider’s decisions are made in absence of perfect knowledge about user preferences. The service provider pursues the strategy of stimulating the demand by offering differentiated prices to the customers. For finding the optimal pricing we apply a stochastic quasi-gradient algorithm that is integrated with a simulation model that drives the evolution of the network and user preferences over time. We show that exploiting the social network structure and implementing differentiated pricing can substantially increase the revenues of a service provider operating on a social network. More generally, we show that stochastic gradient methods represent a powerful methodology for the optimization of decisions in social networks.     

Robust strategies for facility location under uncertainty

This paper considers a stochastic facility location problem in which multiple capacitated facilities serve customers with a single product, and a stockout probabilistic requirement is stated as a chance constraint. Customer demand is assumed to be uncertain and to follow either a normal or an ambiguous distribution. We study robust approximations to the problem in order to incorporate information about the random demand distribution in the best possible, computationally tractable way. We also discuss how a decision maker’s risk preferences can be incorporated in the problem through robust optimization. Finally, we present numerical experiments that illustrate the performance of the different robust formulations. Robust optimization strategies for facility location appear to have better worst-case performance than nonrobust strategies. They also outperform nonrobust strategies in terms of realized average total cost when the actual demand distributions have higher expected values than the expected values used as input to the optimization models.     

A note on continuously decomposed evolving exchange economies

It is routine to demonstrate in the exchange economy framework that small changes of individual preferences and endowments always result in small changes of the derived excess demand functions as one should expect. Though being as desirable for reasons of the consistency of the whole approach, however, a precise proof of the converse direction so far is still open to question. The present paper shows that it is actually true. We use a decomposition method for aggregate excess demand functions developed by Mas-Colell which is derived from the well-known decomposition method developed by Sonnenschein and perfected by Debreu and Mantel. Our result fills in a notorious gap in the line of economic justification usually given for this decomposition, or disaggregation, method in that comparative static analysis would be restricted if the decomposition of excess demand functions would not be continuous.     

风险厌恶下的供应链收益共享契约协调模型研究

收益共享契约是实现供应链系统绩效改善或完美协调的一种机制.考虑了零售商与供应商分别具有风险厌恶决策偏好情况下,在随机市场需求下建立了由单供应商和单零售商组成的二级供应链的收益共享契约模型,并对模型进行了分析,揭示了供应商和零售商的风险厌恶决策偏好对收益共享契约参数的影响.研究结果表明:当销售商(供应商)的风险厌恶控制在...     

Exact SDP reformulations of adjustable robust linear programs with box uncertainties under separable quadratic decision rules via SOS representations of non-negativity

In this paper we show that two-stage adjustable robust linear programs with affinely adjustable data in the face of box data uncertainties under separable quadratic decision rules admit exact semi-definite program (SDP) reformulations in the sense that they share the same optimal values and admit a one-to-one correspondence between the optimal solutions. This result allows adjustable robust solutions of these robust linear programs to be found by simply numerically solving their SDP reformulations. We achieve this result by first proving a special sum-of-squares representation of non-negativity of a separable non-convex quadratic function over box constraints. Our reformulation scheme is illustrated via numerical experiments by applying it to an inventory-production management problem with the demand uncertainty. They demonstrate that our separable quadratic decision rule method to two-stage decision-making performs better than the single-stage approach and is capable of solving the inventory production problem with a greater degree of uncertainty in the demand.

     

Variational Analysis for the Consumer Theory

We look for an interpretation of the demand correspondence in the consumer theory as a generalized derivative of the inverse utility function. We test the main concepts of nonsmooth analysis for such an objective. The proofs only use classical methods in optimization such as penalization and optimality conditions.     

基于对应分析法的不同收入等级居民的消费特征分析——以广东省城镇居民为例

根据2008年广东省不同收入等级城镇居民的人均消费构成的统计数据,采用对应分析法,并结合可支配收入、平均消费倾向分析不同收入等级城镇居民的消费特征.针对不同的收入人群提出了不同的扩大内需措施的政策建议.     

A Comparative Study of Multiple-Objective Metaheuristics on the Bi-Objective Set Covering Problem and the Pareto Memetic Algorithm

Many organizations face employee scheduling problems under conditions of variable demand for service over the course of an operating day and across a planning horizon. These organizations are concerned with the tour scheduling problem that involves assigning shifts and break times to the work days of employees and allocating days off to individual work schedules. Nowadays, organizations try to adopt various scheduling flexibility alternatives to meet the fluctuating service demand. On the other hand, they have also realized that providing employee productivity and satisfaction is as much important as meeting the service demand. Up to date, tour scheduling solution approaches have neglected considering employee preferences and tried to develop work schedules for employees in a subsequent step. This paper presents a goal programming model that implicitly represents scheduling flexibility and also incorporates information about the preferred working patterns of employees. After solving the proposed model, a work schedule will be generated for each employee without requiring a further step for the assignment of shifts, break times, and work days to employees. The model is capable of handling multiple scheduling objectives, and it can produce optimal solutions in very short computing times.     

The impact of two-product joint lifecycles on capacity planning of remanufacturing networks

Capacity planning in the reverse channel of closed-loop supply chains (CLSCs) involves complex issues due to the different lifecycles of product offerings in combination with the variability regarding product usage time, quality level of used products and return patterns. (Georgiadis, P., Vlachos, D., Tagaras, G., 2006. The impact of product lifecycle on capacity planning of closed-loop supply chains with remanufacturing. Production and Operations Management 15; 514–527) developed a system dynamics (SD) model to study a CLSC with remanufacturing for a single product which incorporates a dynamic capacity modeling approach. We extend this SD model for two sequential product-types under two alternative scenarios regarding the market preferences over the product-types; in the first scenario, the market is considered showing no preferences, while in the second scenario, the demand over a product-type can be satisfied only by providing units of the specific type. We study how the joint lifecycles of two product-types, entry time of the second product-type to the market and used product return patterns affect the optimal policies regarding expansion and contraction of collection and remanufacturing capacities. The results of extensive numerical investigation are tested for their statistical significance using analysis of variance (ANOVA). In the first scenario, the results show that the system performs best when the two lifecycles form a trapezoid pattern for total demand while in the second scenario, when the two lifecycles form a triangular pattern.     

Implementing matching rules by type pretension mechanisms

We consider a two-sided matching model where agents' preferences are a function of the types of their potential mates. Matching rules are manipulated by type misrepresentation. We explore the implementability of the -core in -Strong Nash Equilibria. Although direct type pretension mechanisms rule out “bad” equilibria, the existence of equilibrium cannot be generally guaranteed. However, taking as the discrete partition, the individually rational matching correspondence is partially implementable in Nash equilibria. On the other hand, incorporating a certain degree of hypocrisy in the mechanism, i.e., allowing agents to pretend different types to different potential mates, ensures the full implementability of the -core in -Strong Nash Equilibria.     

Introduction of a second channel: Implications for pricing and profits

In this paper we study the optimal pricing strategies when a product is sold on two channels such as the Internet and a traditional channel. We assume a stylized deterministic demand model where the demand on a channel depends on prices, degree of substitution across channels and the overall market potential. We first study four prevalent pricing strategies which differ in the degree of autonomy for the Internet channel. For a monopoly, we provide theoretical bounds for these pricing strategies. We also analyze the duopoly case where an incumbent mixed retailer faces competition with a pure retailer and characterize price equilibria. Finally, through a computational study, we explore the behavior (price and profits) under different parameters and consumer preferences for the alternative channels.