Solution Concepts of N-person Cooperative Games as Points in the Game Space
Author : Richard Decker Spinetto
Publisher :
Page : 134 pages
File Size : 25,51 MB
Release : 1971
Category : Game theory
ISBN :
Author : Richard Decker Spinetto
Publisher :
Page : 134 pages
File Size : 25,51 MB
Release : 1971
Category : Game theory
ISBN :
Author : Imma Curiel
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 26,21 MB
Release : 2013-03-14
Category : Business & Economics
ISBN : 147574871X
In this book applications of cooperative game theory that arise from combinatorial optimization problems are described. It is well known that the mathematical modeling of various real-world decision-making situations gives rise to combinatorial optimization problems. For situations where more than one decision-maker is involved classical combinatorial optimization theory does not suffice and it is here that cooperative game theory can make an important contribution. If a group of decision-makers decide to undertake a project together in order to increase the total revenue or decrease the total costs, they face two problems. The first one is how to execute the project in an optimal way so as to increase revenue. The second one is how to divide the revenue attained among the participants. It is with this second problem that cooperative game theory can help. The solution concepts from cooperative game theory can be applied to arrive at revenue allocation schemes. In this book the type of problems described above are examined. Although the choice of topics is application-driven, it also discusses theoretical questions that arise from the situations that are studied. For all the games described attention will be paid to the appropriateness of several game-theoretic solution concepts in the particular contexts that are considered. The computation complexity of the game-theoretic solution concepts in the situation at hand will also be considered.
Author : Rodica Branzei
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 38,86 MB
Release : 2008-03-08
Category : Business & Economics
ISBN : 354077954X
Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.
Author : John Nash
Publisher : Princeton University Press
Page : 273 pages
File Size : 49,73 MB
Release : 2016-06-29
Category : Mathematics
ISBN : 140088408X
When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive and well. Since then, Sylvia Nasar's celebrated biography A Beautiful Mind, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949. From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness. In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography. The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.
Author : Anatol Rapoport
Publisher : Courier Corporation
Page : 337 pages
File Size : 31,9 MB
Release : 2013-06-17
Category : Mathematics
ISBN : 0486143678
DIVSequel to Two-Person Game Theory introduces necessary mathematical notation (mainly set theory), presents basic concepts and models, and provides applications to social situations. /div
Author : John C. Harsanyi
Publisher : CUP Archive
Page : 340 pages
File Size : 50,16 MB
Release : 1986
Category : Decision-making
ISBN : 9780521311830
This is a paperback edition of a major contribution to the field, first published in hard covers in 1977. The book outlines a general theory of rational behaviour consisting of individual decision theory, ethics, and game theory as its main branches. Decision theory deals with a rational pursuit of individual utility; ethics with a rational pursuit of the common interests of society; and game theory with an interaction of two or more rational individuals, each pursuing his own interests in a rational manner.
Author : William F. Lucas
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 30,57 MB
Release : 1981-12-31
Category : Mathematics
ISBN : 9780821867334
Author : John Eatwell
Publisher : Springer
Page : 275 pages
File Size : 50,48 MB
Release : 1989-09-01
Category : Business & Economics
ISBN : 1349201812
This is an extract from the 4-volume dictionary of economics, a reference book which aims to define the subject of economics today. 1300 subject entries in the complete work cover the broad themes of economic theory. It concentrates on the topic of game theory.
Author : Jeffrey Harlow Grotte
Publisher :
Page : 180 pages
File Size : 37,97 MB
Release : 1974
Category : Differential equations
ISBN :
It is of interest to the study of cooperative game theory to develop models whereby the dynamics of negotiation among the players can be investigated. One approach to this problem concentrates on the use of discrete transfer schemes to study how players might arrive at a desirable outcome. A parallel approach employs systems of differential equations whose solutions represent a continuous transfer of payoff over time. It is the intention of this work to further research in this latter area. Chapter headings include the following: Systems of differential equations with polyhedral stable sets; Applications to cooperative game theory; Nonefficient bargaining systems.
Author : Albert G. Holzman
Publisher : CRC Press
Page : 393 pages
File Size : 34,63 MB
Release : 2020-11-26
Category : Computers
ISBN : 100014612X
This book covers the fundamentals of linear programming, extension of linear programming to discrete optimization methods, multi-objective functions, quadratic programming, geometric programming, and classical calculus methods for solving nonlinear programming problems.