Topics In Mathematical Economics And Game Theory

Topics in Mathematical Economics and Game Theory

Mathematical Methods of Game and Economic Theory

Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.

Topics in Mathematical Economics and Game Theory

Among his contributions to game theory, economics, and mathematics, Aumann introduced the concept of "acceptable points." As this endeared him to many game theorists, a reprint of his seminal 1959 paper on "Acceptable Points in General Cooperative n-Person Games" leads the 17 offerings on cooperative and non-cooperative game theory and economics and social choice. A number of these papers or related works were presented at the Fields Institute Conference, "New Directions in the Theory of Markets and Games," held October 1995 in Toronto honoring Aumann. The conference program concludes the text. Lacks an index. Annotation copyrighted by Book News, Inc., Portland, OR