David Gale

Bio: David Gale is an academic researcher from University of California, Berkeley. The author has contributed to research in topics: Mathematical proof & Stable marriage problem. The author has an hindex of 35, co-authored 94 publications receiving 13310 citations. Previous affiliations of David Gale include Brown University & University of California, San Diego.

College Admissions and the Stability of Marriage

Abstract: (2013). College Admissions and the Stability of Marriage. The American Mathematical Monthly: Vol. 120, No. 5, pp. 386-391.

The theory of linear economic models

Abstract: In the past few decades, methods of linear algebra have become central to economic analysis, replacing older tools such as the calculus. David Gale has provided the first complete and lucid treatment of important topics in mathematical economics which can be analyzed by linear models. This self-contained work requires few mathematical prerequisites and provides all necessary groundwork in the first few chapters. After introducing basic geometric concepts of vectors and vector spaces, Gale proceeds to give the main theorems on linear inequalities?theorems underpinning the theory of games, linear programming, and the Neumann model of growth. He then explores such subjects as linear programming; the theory of two-person games; static and dynamic theories of linear exchange models, including problems of equilibrium prices and dynamic stability; and methods of play, optimal strategies, and solutions of matrix games. This book should prove an invaluable reference source and text for mathematicians, engineers, economists, and those in many related areas.

The Theory of Linear Economic Models

Abstract: In the past few decades, methods of linear algebra have become central to economic analysis, replacing older tools such as the calculus. David Gale has provided the first complete and lucid treatment of important topics in mathematical economics which can be analyzed by linear models. This self-contained work requires few mathematical prerequisites and provides all necessary groundwork in the first few chapters. After introducing basic geometric concepts of vectors and vector spaces, Gale proceeds to give the main theorems on linear inequalities—theorems underpinning the theory of games, linear programming, and the Neumann model of growth. He then explores such subjects as linear programming; the theory of two-person games; static and dynamic theories of linear exchange models, including problems of equilibrium prices and dynamic stability; and methods of play, optimal strategies, and solutions of matrix games. This book should prove an invaluable reference source and text for mathematicians, engineers, economists, and those in many related areas.

Multi-Item Auctions

Abstract: A collection of items is to be distributed among several bidders, and each bidder is to receive at most one item. Assuming that the bidders place some monetary value on each of the items, it has been shown that there is a unique vector of equilibrium prices that is optimal, in a suitable sense, for the bidders. In this paper we describe two dynamic auction mechanisms: one achieves this equilibrium and the other approximates it to any desired degree of accuracy.

Increasing Returns and Long-Run Growth

Abstract: This paper presents a fully specified model of long-run growth in which knowledge is assumed to be an input in production that has increasing marginal productivity. It is essentially a competitive equilibrium model with endogenous technological change. In contrast to models based on diminishing returns, growth rates can be increasing over time, the effects of small disturbances can be amplified by the actions of private agents, and large countries may always grow faster than small countries. Long-run evidence is offered in support of the empirical relevance of these possibilities.

The Design and Analysis of Computer Algorithms

Abstract: From the Publisher: With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter. 0201000296B04062001

Graph theory with applications

Abstract: (1977). Graph Theory with Applications. Journal of the Operational Research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.

Convex bodies : the Brunn-Minkowski theory

Abstract: 1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.