» Fixed Point Theorems with Applications to Economics and Game Theory
Rating: 4.5 / 5.00 (2 reviews)
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Manufacturer: Cambridge University Press
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Fixed Point Theorems with Applications to Economics and Game Theory Details
Binding: PaperbackDewey Decimal Number: 330
EAN: 9780521388085
ISBN: 0521388082
Label: Cambridge University Press
Manufacturer: Cambridge University Press
Number Of Items: 1
Number Of Pages: 144
Publication Date: 1989-07-28
Publisher: Cambridge University Press
Studio: Cambridge University Press
Fixed Point Theorems with Applications to Economics and Game Theory Reviews
Customer Rating:
Summary: An excellent survey of more than fixed point theorems.
Comment: 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.
Customer Rating:
Summary: the best buy
Comment: The author, one of the most prominet professors in mathematical economics surveyed fixed point theorems. The theorems are often used to prove the existence of solutions in game theory and economics. If you major in mathematical economics or game theory, you can't avoid to buy this book.
Editorial Review for Fixed Point Theorems with Applications to Economics and Game Theory:
One of the problems in economics to which economists have devoted a considerable amount of attention in recent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it must be asked under what circumstances such an equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems. These outline 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 cooperative and non-cooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. In addition, the author presents new proofs of old results in order to further clarify the results. He also proposes new 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.