Download or read book Values of Non Atomic Games written by Robert J. Aumann and published by Princeton University Press. This book was released on 2015-03-08 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "Shapley value" of a finite multi- person game associates to each player the amount he should be willing to pay to participate. This book extends the value concept to certain classes of non-atomic games, which are infinite-person games in which no individual player has significance. It is primarily a book of mathematics—a study of non-additive set functions and associated linear operators. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Values of Non atomic Games I written by R.J. Aumann and published by . This book was released on 1968 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Values of Non atomic Games written by Robert J. Aumann and published by . This book was released on 1969 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper reports the second study in a series concerned with the value of participation in a non-atomic game. A non-atomic game is a special type of infinite-person game in which no individual player has significant influence on the outcome. The work develops the concept of mixing value and presents a new approach based on mixing transformations. A program is outlined for imposing a probability measure on the space of all measurable orders. Some consideration is given to the asymptotic approach, in which a game with a continuum is treated as a limit of games with finitely many players. It is significant that all values defined in the axiomatic, mixing, and asymptotic approaches possess a common diagonal property.
Download or read book Potential in Non atomic Games written by Timothy Douglas Watson and published by . This book was released on 1994 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Value of the Non atomic Game Arising from a Rate setting Application and Related Problems written by Joseph Raanan and published by . This book was released on 1978 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work is motivated by the following problem: bulk-service telephone lines were installed at Cornell University, to be used for long-distance calls. The charges paid to the telephone company are mostly fixed monthly charges and are not usage-related. The problem is how to allocate these costs back to the users in a per call fashion, and how to do it in a way that is fair and efficient. The problem was solved by using the value of the associated non-atomic game. To be able to do this, the theory of non-atomic games had to be extended by weakening certain differentiability requirements. This is done here; in addition a number of results about full-range game are obtained. Next the problem of non-atomic linear production games is studied. A number of results about the cores of such games are obtained, extending and strengthening similar results about finite linear production games. In addition, some results about the value of such games are established, and relationships between the core and the value are derived for a special case. (Author).
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book The Shapley value written by Alvin E. Roth and published by Cambridge University Press. This book was released on 1988-10-28 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume makes accessible the large body of work that has grown out of Shapley's seminal 1953 paper.
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Game Theory written by Guillermo Owen and published by Emerald Group Publishing. This book was released on 2013-08-08 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game Theory has served as a standard text for game theory courses since the publication of the First Edition in 1968. The Fourth Edition updates several recently developed subfields.
Download or read book Handbook of the Shapley Value written by Encarnación Algaba and published by CRC Press. This book was released on 2019-12-06 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953. The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory. Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation." Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.
Download or read book Inside the Economist s Mind written by Paul A. Samuelson and published by John Wiley & Sons. This book was released on 2009-02-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: By focusing on the human side as well as the intellectualdimensions of how economists work and think, this collection ofinterviews with top economists of the 20th century becomes astartling and lively introduction to the modern world ofmacroeconomics. A fun read! For more information, frequent updates, and to comment on theforthcoming book, visit William A. Barnett's weblog athttp://economistmind.blogspot.com/. Acclaim for Inside the Economist's Mind "In candid interviews, these great economists prove to befabulous story tellers of their lives and times. Unendinglygripping for insiders, this book should also help non-specialistsunderstand how economists think." Professor Julio Rotemberg, Harvard University Business School,and Editor, Review of Economics and Statistics. "Economics used to be called the 'dismal science'. It will beimpossible for anybody to hold that view anymore ... This isscience with flesh and blood, and a lot of fascinating stories thatyou will find nowhere else." Dr. Jean-Pascal Bénassy, Paris-Jourdan SciencesÉconomiques, Paris, France "This book provides a rare and intriguing view of the personaland professional lives of leading economists ... It is like ABeautiful Mind, scaled by a factor of 16 [the number ofinterviews in the book]." Professor Lee Ohanian, University of California at LosAngeles " ... if you want an insider view of how economics has beendeveloping in the last decades, this is the (only) book foryou." Professor Giancarlo Gandolfo, University of Rome ‘LaSapienza,’ Rome "Here we see the HUMAN side of path-breaking research, thepersonalities and pitfalls, the DRAMA behind the science." Professor Francis X. Diebold, University of Pennsylvania,Philadelphia
Download or read book Collected Papers written by Robert J. Aumann and published by MIT Press. This book was released on 2000 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert Aumann's career in game theory has spanned over research - from his doctoral dissertation in 1956 to papers as recent as January 1995. Threaded through all of Aumann's work (symbolized in his thesis on knots) is the study of relationships between different ideas, between different phenomena, and between ideas and phenomena. "When you look closely at one scientific idea", writes Aumann, "you find it hitched to all others. It is these hitches that I have tried to study". The papers are organized in several categories: general, knot theory, decision theory (utility and subjective probability), strategic games, coalitional games, and mathematical methods. Aumann has written an introduction to each of these groups that briefly describes the content and background of each paper, including the motivation and the research process, and relates it to other work in the collection and to work by others. There is also a citation index that allows readers to trace the considerable body of literature which cites Aumann's own work.
Download or read book Economics 4 volumes written by David A. Dieterle and published by Bloomsbury Publishing USA. This book was released on 2017-03-27 with total page 2345 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive four-volume resource that explains more than 800 topics within the foundations of economics, macroeconomics, microeconomics, and global economics, all presented in an easy-to-read format. As the global economy becomes increasingly complex, interconnected, and therefore relevant to each individual, in every country, it becomes more important to be economically literate—to gain an understanding of how things work beyond the microcosm of the economic needs of a single individual or family unit. This expansive reference set serves to establish basic economic literacy of students and researchers, providing more than 800 objective and factually driven entries on all the major themes and topics in economics. Written by leading scholars and practitioners, the set provides readers with a framework for understanding economics as mentioned and debated in the public forum and media. Each of the volumes includes coverage of important events throughout economic history, biographies of the major economists who have shaped the world of economics, and highlights of the legislative acts that have shaped the U.S. economy throughout history. The extensive explanations of major economic concepts combined with selected key historical primary source documents and a glossary will endow readers with a fuller comprehension of our economic world.
Download or read book Topics in Mathematical Economics and Game Theory written by Robert J. Aumann and published by American Mathematical Soc.. This book was released on 1999 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of "Theory of Games and Economic Behavior" by von Neumann and Morgenstern, the concept of games has played an increasing role in economics. It also plays a role of growing importance in other sciences, including biology, political science, and psychology. Many scientists have made seminal advances and continue to be leaders in the field, including Harsanyi, Shapley, Shubik, and Selten. Professor Robert Aumann, in addition to his important contributions to game theory and economics, made a number of significant contributions to mathematics. This volume provides a collection of essays in mathematical economics and game theory, including cutting-edge research on noncooperative game theory and its foundations, bargaining theory, and general equilibrium theory. Also included is a reprint of Aumann's classic paper, "Acceptable Points in General Cooperative n-Person Games" and of the oft-cited, yet hard to find, paper by Maschler, "The Worth of a Cooperative Enterprise to Each Member". This book illustrates the wide range of applications of mathematics to economics, game theory, and social choice. The volume is dedicated to Professor Robert J. Aumann, Hebrew University, Jerusalem, Israel, for his contributions in mathematics and social sciences.
Download or read book Economic Thinkers written by David A. Dieterle and published by Bloomsbury Publishing USA. This book was released on 2013-08-08 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Who are the individuals whose novel ideas, writings, and philosophies have influenced economics throughout history—and in doing so, have helped change the world? This encyclopedia provides a readable study of economics by examining the great economists themselves. This book presents biographies of 200 economic thinkers throughout history, supplying a one-stop reference about the men and women whose ideas, writings, and philosophies created the foundation of our current understanding of economics. Depicting their subjects within the contexts of history, development economics, and econometrics, these biographies provide an insightful overview of the world of economics through the economists of significance and the many subdisciplines, topics, eras, and philosophies they represent. Economic Thinkers: A Biographical Encyclopedia begins by describing economic thinkers in ancient Greece and Rome, moves through history to cover economists in the 15th through 19th centuries, and addresses economic theory in the 20th century and the modern era. Written to be easily accessible and highly readable, the work will appeal to students, scholars, general readers, and anyone interested in learning about the historical and philosophical foundation of economics.
Download or read book Game Theoretic Methods in General Equilibrium Analysis written by J.F. Mertens and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: JEAN-FRANQOIS MERTENS This book presents a systematic exposition of the use of game theoretic methods in general equilibrium analysis. Clearly the first such use was by Arrow and Debreu, with the "birth" of general equi librium theory itself, in using Nash's existence theorem (or a generalization) to prove the existence of a competitive equilibrium. But this use appeared possibly to be merely tech nical, borrowing some tools for proving a theorem. This book stresses the later contributions, were game theoretic concepts were used as such, to explain various aspects of the general equilibrium model. But clearly, each of those later approaches also provides per sea game theoretic proof of the existence of competitive equilibrium. Part A deals with the first such approach: the equality between the set of competitive equilibria of a perfectly competitive (i.e., every trader has negligible market power) economy and the core of the corresponding cooperative game.
Download or read book Game and Economic Theory written by Sergiu Hart and published by University of Michigan Press. This book was released on 1995 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outstanding works showing the application of game theory to economic theory.
