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» » Fixed Point Theorems with Applications to Economics and Game Theory
Fixed Point Theorems with Applications to Economics and Game Theory e-book

Author:

Kim C. Border

Language:

English

Category:

Math

Subcategory:

Mathematics

ePub size:

1259 kb

Other formats:

lrf mbr lrf mobi

Rating:

4.2

Publisher:

Cambridge University Press (April 26, 1985)

Pages:

140

ISBN:

0521265649

Fixed Point Theorems with Applications to Economics and Game Theory e-book

by Kim C. Border


New minimax inequality with applications to existence theorems of equilibrium points.

New minimax inequality with applications to existence theorems of equilibrium points. Journal of Optimization Theory and Applications, Vol. 82, Issue. This book provides a clear exposition of the most important results and techniques of fixed point theory with applications to many areas of current interest in analysi. t is a well written boo. he material is completed by well collected exercises at the end of every chapter.

The book cleanly separates the mathematical theory from the economic applications. Mathematicians, as well as economists, will value this book as a basic, helpful handbook on finite-dimensional fixed-point theorems. Perhaps the book's greatest strength is that the level of mathematical sophistication it requires is uniform throughout. Timothy J. Kehoe, Journal of Economic Literature.

Book by American Mathematical Society Short Course, Game Theory and its Applications (1979 : Biloxi. This book both summarizes the basic theory of evolutionary games and explains their developing. Materials for High Temperature Power Generation and Process Plant Applications. 59 MB·31,745 Downloads·New! and process plant applications presented at Materials Congress 98 Frontiers in Material Science and Technology. Living Well with Chronic Disease: A Call for Public Health Action. How to Write a Better Thesis. 84 MB·217,090 Downloads.

An introduction to fixed point theory, a body of mathematical techniques for proposing conditions under which sets of. .

An introduction to fixed point theory, a body of mathematical techniques for proposing conditions under which sets of assumptions (underlying economic models) have solutions. Lists with This Book. This book is not yet featured on Listopia.

Fixed point theorems are the basic mathematical tools used in showing the existence of solution concepts in game theory and economics. These notes are intended to be a nonintimidating intro­ duction to the subject of fixed point theory with particular emphasis on economic applications. While I have tried to integrate the mathematics and applications, these notes are not a comprehensive introduction to either general equilibrium theory or game theory

Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity.

1987 ; Vol. 25. pp. 1870-1872. publisher "American Economic Association", } ty - jour. AU - Kehoe, Timothy J. PY - 1987.

One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible.

Fudenberg, Drew and Jean Tirole Game Theory, MIT Press Kakutani, S. A Generalization of Brouwer’s Fixed Point Theorem, Duke Mathematical Journal 8 : 457–459.

Fudenberg, Drew and Jean Tirole Game Theory, MIT Press. Green, Jerry R. and Walter P. Heller Mathematical Analysis and Convexity with Applications to Economics, in Handbook of Mathematical Economics, eds. Kenneth J. Arrow and Michael D. Intriligator, Vol. 1, North-Holland, pp. 15–52. Kakutani, S. Kreps, David M. Nash Equilibrium, in The New Palgrave: Game Theory, eds. John Eatwell, Murray Milgate, and Peter Newman, W. W. Norton, pp. 167–177. Game.

One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. The author presents topical proofs of old results in order to further clarify the results. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students.
Gadar
The author compiles theorems, definitions, and properties on a number of topics. There's some convex analysis, maximization of binary relations, fixed point and selection theorems, and various sufficient conditions for existence of equilibria in games and economies.
A nice feature is that the author explains the equivalence or interconnectedness of theorems from different classes -- comparing the KMM lemma to Brouwer's fixed pt. thm., for instance.
This book is extremely useful for its many variations on common principles. Researchers can benefit from consulting it when they have a problem which does not satisfy the usual criteria -- for instance, if you ever have to ask, "I have a correspondence which satisfies all the conditions for Kakutani's theorem except that it is l.h.c. rather than u.h.c.; am I still able to guarantee a fixed point?"
Grad students in micro/game theory can benefit from the survey of theorems, and familiarizing themselves with the many ways they can get to desired results.
The book is compact and thorough with little exposition. Definitions are very clear, and the author is very good at noting when definitions vary, or the same term has multiple definitions in the literature. Though it presents itself as a mathematical text, its audience is clearly economists -- the conditions given and situations described are clearly ones that economists will recognize, and the applications are economic.
A very nice book for people who already know the applications of such theorems and who need minimal explanation.
Qus
This book is an awesome reference for economists or those interested in game theory. It is highly mathematical, so if your mathematical maturity is not very high I would not recommend this book for you. I am finishing up my masters in mathematics and some of it was slow reading even for me. However, if you would be able to read the mathematics I highly recommend it.

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