Supermodularity and Complementarity

Supermodularity and Complementarity

Author: Donald M. Topkis

Publisher: Princeton University Press

Published: 2011-02-11

Total Pages: 285

ISBN-13: 140082253X

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The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity. This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.


Supermodularity and Complementarity in Economics

Supermodularity and Complementarity in Economics

Author: Rabah Amir

Publisher:

Published: 2007

Total Pages: 0

ISBN-13:

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The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analysis of games with strategic complementarities. The results are presented in a simplified yet rigourous manner, without reference to lattice theory, for the special case of onedimensional parameter and actions sets, with the emphasis being on wide accessibility. Detailed applications are presented for well-known models of consumer behavior, monopoly pass-through, Bertrand and Cournot competition, strategic R&D, search and matching. Wherever appropriate, useful tricks for applications and comparative comments are inserted.


Putting Auction Theory to Work

Putting Auction Theory to Work

Author: Paul Milgrom

Publisher: Cambridge University Press

Published: 2004-01-12

Total Pages: 378

ISBN-13: 1139449168

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This book provides a comprehensive introduction to modern auction theory and its important new applications. It is written by a leading economic theorist whose suggestions guided the creation of the new spectrum auction designs. Aimed at graduate students and professionals in economics, the book gives the most up-to-date treatments of both traditional theories of 'optimal auctions' and newer theories of multi-unit auctions and package auctions, and shows by example how these theories are used. The analysis explores the limitations of prominent older designs, such as the Vickrey auction design, and evaluates the practical responses to those limitations. It explores the tension between the traditional theory of auctions with a fixed set of bidders, in which the seller seeks to squeeze as much revenue as possible from the fixed set, and the theory of auctions with endogenous entry, in which bidder profits must be respected to encourage participation.


Matching with Transfers

Matching with Transfers

Author: Pierre-André Chiappori

Publisher: Princeton University Press

Published: 2020-05-26

Total Pages: 262

ISBN-13: 0691203504

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Over the past few decades, matching models, which use mathematical frameworks to analyze allocation mechanisms for heterogeneous products and individuals, have attracted renewed attention in both theoretical and applied economics. These models have been used in many contexts, from labor markets to organ donations, but recent work has tended to focus on "nontransferable" cases rather than matching models with transfers. In this important book, Pierre-André Chiappori fills a gap in the literature by presenting a clear and elegant overview of matching with transfers and provides a set of tools that enable the analysis of matching patterns in equilibrium, as well as a series of extensions. He then applies these tools to the field of family economics and shows how analysis of matching patterns and of the incentives thus generated can contribute to our understanding of long-term economic trends, including inequality and the demand for higher education.


Oligopoly Pricing

Oligopoly Pricing

Author: Xavier Vives

Publisher: MIT Press (MA)

Published: 1999

Total Pages: 446

ISBN-13: 9780262220606

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Applies a modern game-theoretic approach to develop a theory of oligopoly pricing. The text relates classic contributions to the field of modern game theory and discusses basic game-theoretic tools and equilibrium, paying particular attention to developments in the theory of supermodular games.


Complementarity, Improvement Programs and Queuing Technology

Complementarity, Improvement Programs and Queuing Technology

Author: Phillip J. Lederer

Publisher:

Published: 2011

Total Pages: 0

ISBN-13:

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During the past two decades firms have adopted many types of functional improvement programs. A goal of this paper is to study interactions of operations programs with improvement programs in other functions. An important issue is whether these programs are complements (or substitutes): that is, whether implementation of a pair of programs adds more value (or loses value) than the sum of the individual programs. Recent advances based upon Topkis's (1998) theory of supermodularity have created a framework to establish sufficient conditions to guarantee that two interacting activities or programs are complementary. But not all programs can be characterized by supermodularity. In particular, I show that programs that involve uncertainty reduction do not fit the supermodularity framework with respect to other programs. In the absence of supermodularity, complementarity properties can sometimes be established, but some assumption about the production function must be assumed. Assuming that production is based upon queuing technology, three programs are studied and I show that complement/substitute properties can be established. The three programs are uncertainty reduction about a key demand parameter, elimination of biased estimates of cost and direct cost savings. I show that uncertainty reduction and bias removal can be complements or substitutes; but, uncertainty reduction and cost estimation bias elimination are both complementary to direct cost savings. Also, several operations improvement programs are shown to be complementary to each other. The fact that the operations improvement programs are complementary to all other programs is significant for the organizational design of capital budgeting, as this assures that the true project value is higher than its standalone net present value. Results are generalized by presenting conditions that assure the complementarity or substitutability of these three types of programs. Because batching/lot sizing and any fixed charge problem (such as facility location) have cost structures similar to queuing, the results are shown to apply to a broad range of technologies.


Iterative Methods in Combinatorial Optimization

Iterative Methods in Combinatorial Optimization

Author: Lap Chi Lau

Publisher: Cambridge University Press

Published: 2011-04-18

Total Pages: 255

ISBN-13: 1139499394

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With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.


Innovative Forms of Organizing

Innovative Forms of Organizing

Author: Andrew M Pettigrew

Publisher: SAGE

Published: 2003-07-17

Total Pages: 443

ISBN-13: 1412933161

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This book presents novel theoretical ideas and empirical findings where the fields of strategizing and organizing meet. At this boundary lie many of the most crucial theoretical and practical issues for management and managing. Innovative Forms of Organizing, the eagerly awaited sequel to The Innovating Organization (SAGE, 2000), draws upon the comprehensive data sets of the INFORM programme of research, to examine the development of innovative forms of organizing and company performance in organizations across Europe, Japan and the United States. Innovative Forms of Organizing establishes and develops three strong themes: organizing and strategizing; complementarities, change and performance; and the management of dualities in the modern corporation. The book then discusses the implications of its presented ideas for strategizing/organizing in the 21st century firm and the challenges for management researchers of conducting large scale, international comparative research. Innovative Forms of Organizing thereby illustrates 21st Century management research in 21st Century organizations across Europe, Japan and the USA. This seminal international study will be a classic in the field for years to come for scholars and policy makers in academia, business and government who are interested in strategy, organization and international management.