Fixed point theorems with applications to economics and game theory. (English) Zbl 0558.47038

Border, Kim C.

Cambridge etc.: Cambridge University Press. VIII, 129 p. £17.50; $ 29.95 (1985).

The title of the monograph reflects well the contents, provided ”with” is interpreted as ”that have”. Indeed, the book displays in detail that part of the theory of fixed points which is widely used in mathematical economics and game theory. This includes fixed points of correspondences, i.e., set-valued functions. Thus, contraction principles and infinite dimensional considerations, very useful in equations, are not touched upon. Computation schemes, primarily developed for use in economic theory, are not presented either. What is given is carefully presented, with the needed background, the interconnections among the different techniques and with a brief glance at the applications themselves. The emphasis is on the geometric intuition (and at some points the reader’s intuition is employed instead of detailed analysis). The presentation is quite formal, and emphasis is on making things elementary which is very convenient for students.

Reviewer: Z.Artstein

MSC:

47H10	Fixed-point theorems
47-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
91B50	General equilibrium theory
91A12	Cooperative games
47H05	Monotone operators and generalizations
90-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming

Keywords:

mathematical economics; game theory; fixed points of correspondences; set-valued functions