Costly information acquisition under horizontal competition

We analyze endogenous acquisition of costly information for two firms that sell homogeneous products. Prior to determining its production quantity, either firm has an opportunity to acquire a costly forecast. There exists a correlation between errors in the acquired forecasts. We model the problem as a two-stage game in which the firms first decide whether to acquire their respective forecasts and then decide their production quantities. We derive the equilibrium outcome on information acquisition and production quantity.     

Endogenous information acquisition in supply chain management

In this paper, we analyze an endogenous determination of efforts put into information acquisition and its impact on supply chain management. More specifically, we consider a supplier who sells a product to a buyer during a single selling season. Prior to placing an order with the supplier, the buyer has an option to acquire additional information about the demand by hiring experts (who are capable of providing forecasts). Because a commission fee must be paid to each hired expert, there exists a tradeoff between the cost and the value of the information, and the buyer needs to determine how much information to acquire. We derive the optimal information-acquisition level in an integrated setting and compare it with that determined in a decentralized setting. We also analyze several types of supply contracts to examine if they can coordinate the supply chain and allow an arbitrary division of system profit between the supplier and the buyer.     

Optimal contracts under endogenous demand information acquisition

We consider a supplier selling to a retailer who decides whether or not to exert a fixed cost to acquire private demand information. We show that quantity discounts, established by the extant literature to be the optimal response for exogenous information acquisition, are also optimal under the setting with endogenous information acquisition.     

The properties of a stochastic optimal sequential strategy for purchasing information in a project selection problem

In this article we employ the results of Fatti et al. (1987) on the expected value of sample infomation [EVSI] for a class of economic problems dealing with one source of information and a decision to reject or accept an investment project. We consider a framework which allows for the purchasing of many types of costly information aimed at reducing the uncertainty regarding the project's monetary value. The optimal information-seeking strategy is evaluated for a neutral risk taker. Moreover, its upper bound is derived for some special cases.     

The optimal solution of multi-kernel regularization learning

In regularized kernel methods, the solution of a learning problem is found by minimizing a functional consisting of a empirical risk and a regularization term. In this paper, we study the existence of optimal solution of multi-kernel regularization learning. First, we ameliorate a previous conclusion about this problem given by Micchelli and Pontil, and prove that the optimal solution exists whenever the kernel set is a compact set. Second, we consider this problem for Gaussian kernels with variance σ∈(0,∞), and give some conditions under which the optimal solution exists.     

The rational weakness of strong ties: Failure of group solidarity in a highly cohesive group of rational agents

Recent research (Flache, 1996; Flache and Macy, 1996) suggests a "weakness of strong ties." Cohesive social networks may undermine group solidarity, rather than sustain it. In the original analysis, simulations showed that adaptive actors learn cooperation in bilateral exchanges faster than cooperation in more complex group exchanges, favoring ties at the expense of the common good. This article uses game theory to demonstrate that cognitive simplicity is not a scope condition for the result. The game theoretical analysis identifies a new condition for the failure of group solidarity in a cohesive group. Task uncertainty may make rational cooperation increasingly inefficient in common good production. Accordingly, rational actors may increasingly sacrifice benefits from common good production in order to maintain social ties, as their dependence on peer approval rises.     

The flow complex: A data structure for geometric modeling

We study a special case of the critical point (Morse) theory of distance functions namely, the gradient flow associated with the distance function to a finite point set in . The fixed points of this flow are exactly the critical points of the distance function. Our main result is a mathematical characterization and algorithms to compute the stable manifolds, i.e., the inflow regions, of the fixed points. It turns out that the stable manifolds form a polyhedral complex that shares many properties with the Delaunay triangulation of the same point set. We call the latter complex the flow complex of the point set. The flow complex is suited for geometric modeling tasks like surface reconstruction.     

A comparative analysis of learning curves: Implications for new technology implementation management

New technology implementation projects are notoriously over time and budget resulting in significant financial and strategic organizational consequences. Some argue that inadequate planning and management, misspecification of requirements, team capabilities and learning contribute to cost and schedule over runs. In this paper we examine how learning curve theory could inform better management of new technology implementation projects. Our research makes four important contributions: (1) It presents a comparative analysis of learning curves and proposes how they can be used to help ERP implementation planning and management. (2) Based on empirical data from four ERP implementation projects, it provides illustrations of how managers can apply the curves in different project situations. (3) It provides a theoretical basis for empirical studies of learning and ERP (and other IT) implementations in different organizational settings. (4) It provides empirical justification for the development of learning curve theory in IT implementation.     

Interpreting supply chain dynamics: A quasi-chaos perspective

Chaotic phenomena, chaos amplification and other interesting nonlinear behaviors have been observed in supply chain systems. Chaos can be defined theoretically if the dynamics under study are produced only by deterministic factors. However, deterministic settings rarely present themselves in reality. In fact, real data are typically unknown. How can the chaos theory and its related methodology be applied in the real world? When the demand is stochastic, the interpretation and distribution of the Lyapunov exponents derived from the effective inventory at different supply chain levels are not similar to those under deterministic demand settings. Are the observed dynamics of the effective inventory random, chaotic, or simply quasi-chaos? In this study, we investigate a situation whereby the chaos analysis is applied to a time series as if its underlying structure, deterministic or stochastic, is unknown. The result shows clear distinction in chaos characterization between the two categories of demand process, deterministic vs. stochastic. It also highlights the complexity of the interplay between stochastic demand processes and nonlinear dynamics. Therefore, caution should be exercised in interpreting system dynamics when applying chaos analysis to a system of unknown underlying structure. By understanding this delicate interplay, decision makers have the better chance to tackle the problem correctly or more effectively at the demand end or the supply end.     

The compact-open topology: A new perspective

This paper studies the compact-open topology on the set KC(X) of all real-valued functions defined on a Tychonoff space, which are continuous on compact subsets of X. In addition to metrizability, separability and second countability of this topology on KC(X), various kinds of topological properties of this topology are studied in detail. Actually the motivation for studying the compact-open topology on KC(X) lies in the attempt of having a simpler proof for the characterization of a completeness property of the compact-open topology on C(X), the set of all real-valued continuous functions on X.     

The structure of stratified systems and the structure of mobility: A first approximation to a structural theory of vertical mobility

This essay summarizes an inquiry that explores relations between the structure of stratified systems and the processes of vertical mobility. The inquiry considers economic stratification (the distribution of wealth) and is directed to determining whether the structural properties of stratification systems are sufficient to generate basic patterns in vertical mobility observed in empirical research, especially, the rank‐distance effect. In particular, the question is whether these patterns can be generated even if movement is constrained by nothing more than the size of the population over which wealth is distributed and the total amount of wealth to be distributed. Our results show that the rank‐distance effect emerges even under these minimal assumptions and, further, that rates and distances of vertical mobility are closely related to changes in these boundary parameters of a stratified system. The basic theory developed to relate structure and mobility provides results that are highly consistent with many empirical observations. It also challenges existing claims concerning the nature of the mechanisms determining the relative status immobility of most people in large scale systems. The theory implies that the way in which system structure constrains opportunity for movement is, by itself, sufficient to produce this result and others commonly observed.     

The Hauptsatz for Stratified Comprehension: A Semantic Proof

We prove the cut-elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i. e. Quine's NF minus extensionality. Mathematics Subject Classification: 03B15, 03F05.     

A hyperbolicity criterion for periodic solutions of functional-differential equations: The case of rational periods

We establish necessary and sufficient conditions for hyperbolicity of periodic solutions of nonlinear functional-differential equations.     

The nurse rostering problem: A critical appraisal of the problem structure

This paper is concerned with the problem of nurse rostering within hospitals. We analyse a class of four benchmark instances from the nurse rostering literature to provide insight into the nature of the problem. By highlighting the structure of the problem we are able to reduce the relevant solution space. A mixed integer linear programme is then able to find optimal solutions to all four instances of this class of benchmark problems, each within half an hour. Our second contribution is to extend current mathematical approaches to nurse rostering to take better account of the practical considerations. We provide a methodology for handling rostering constraints and preferences arising from the continuity from one scheduling period to the next.     

The sequence method for finding solutions to infinite games: A first demonstrating example

A noncooperative infinite game can be approached by a sequence of discrete games. For each game in the sequence, a Nash solution can be found as well as their limit. This idea and procedure was used before as a theoretical device to prove existence of solutions to games with continuous payoffs and recently even for a class of games with discontinuous ones (Dasgupta and Maskin, 1981). No one, however, used the method for the actual solution of a game. Here, an example demonstrates the method's usefulness in finding a solution to a two-person game on the unit square with discontinuous payoff functions.The author wishes to thank D. McFadden for very useful discussions. Financial support was provided in part by NSF Grant No. SOC-72-05551A02 to the University of California, Berkeley, California.     

A Contextualized Historical Analysis of the Kuhn–Tucker Theorem in Nonlinear Programming: The Impact of World War II

When Kuhn and Tucker proved the Kuhn–Tucker theorem in 1950 they launched the theory of nonlinear programming. However, in a sense this theorem had been proven already: In 1939 by W. Karush in a master's thesis, which was unpublished; in 1948 by F. John in a paper that was at first rejected by the Duke Mathematical Journal; and possibly earlier by Ostrogradsky and Farkas. The questions of whether the Kuhn-Tucker theorem can be seen as a multiple discovery and why the different occurences of the theorem were so differently received by the mathematical communities are discussed on the basis of a contextualized historical analysis of these works. The significance of the contexts both mathematically and socially for these questions is discussed, including the role played by the military in the shape of Office of Naval Research (ONR) and operations research (OR). Copyright 2000 Academic Press.En démontrant, en 1950, le théorème qui porte aujourd'hui leur nom, Kuhn et Tucker ont donné naissance à la théorie de la programmation non-linéaire. Cependant, en un sens, ce théorème avait été démontré auparavant, d'abord par W. Karush en 1939 dans un mémoire de maîtrise inédit, par la suite par F. John en 1948 dans un article qui avait d'abord été rejeté par le Duke Mathematical Journal, et peut-être même plus tôt par Ostrogradsky et aussi par Farkas. Le présent article cherche à élucider deux questions: Peut-on considérer le théorème Kuhn–Tucker comme un exemple de découverte multiple? Et pourquoi le théorème a-t-il été reçu si différemment dans les diverses communautés mathématiques? Notre discussion se base sur une analyse historique contextuelle des différents ouvrages. Nous examinons ici l'importance du contexte, tant du point de vue des mathématiques que du point de vue social, y compris le rôle joué par le secteur militaire dans le cadre de l'Office of Naval Research et de la recherche opérationnelle. Copyright 2000 Academic Press.MSC 1991 subject classification: 01A60; 49-03; 52-03; 90-03; 90C30.