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.

Complementarity, Equilibrium, Efficiency and Economics
Complementarity, Equilibrium, Efficiency and Economics

Author: G. Isac

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 458

ISBN-13: 1475736231

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In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

Economics of the Family
Economics of the Family

Author: Martin Browning

Publisher: Cambridge University Press

Published: 2014-06-05

Total Pages: 511

ISBN-13: 1107728924

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The family is a complex decision unit in which partners with potentially different objectives make consumption, work and fertility decisions. Couples marry and divorce partly based on their ability to coordinate these activities, which in turn depends on how well they are matched. This book provides a comprehensive, modern and self-contained account of the research in the growing area of family economics. The first half of the book develops several alternative models of family decision making. Particular attention is paid to the collective model and its testable implications. The second half discusses household formation and dissolution and who marries whom. Matching models with and without frictions are analyzed and the important role of within-family transfers is explained. The implications for marriage, divorce and fertility are discussed. The book is intended for graduate students in economics and for researchers in other fields interested in the economic approach to the family.

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.

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.

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.

A Theory of Games with General Complementarities
A Theory of Games with General Complementarities

Author: Filippo L. Calciano

Publisher: Presses univ. de Louvain

Published: 2010-09

Total Pages: 81

ISBN-13: 2874632430

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In the current theory of games, the formal notion of complementarity that is employed is unsatisfactory because it bears too few connections with our intuitive idea of complementarity. This is the starting point of the present work.