Fixed Point Theorems with Applications to Economics and Game Theory

Rating:
Summary: An excellent survey of more than fixed point theorems.
Review: 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.

Rating:
Summary: the best buy
Review: 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.