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Values of Non-Atomic Games

Values of Non-Atomic Games
Author: Robert J. Aumann
Publisher: Princeton University Press
Total Pages: 348
Release: 2015-03-08
Genre: Mathematics
ISBN: 1400867088

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The "Shapley value" of a finite multi- person game associates to each player the amount he should be willing to pay to participate. This book extends the value concept to certain classes of non-atomic games, which are infinite-person games in which no individual player has significance. It is primarily a book of mathematics—a study of non-additive set functions and associated linear operators. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.


Values of Non-atomic Games

Values of Non-atomic Games
Author: Robert J. Aumann
Publisher:
Total Pages: 15
Release: 1970
Genre:
ISBN:

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Values of Non-atomic Games

Values of Non-atomic Games
Author: Robert J. Aumann
Publisher:
Total Pages: 40
Release: 1970
Genre:
ISBN:

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Values of Non-atomic Games, Part I: the Axiomatic Approach

Values of Non-atomic Games, Part I: the Axiomatic Approach
Author: Robert J. Aumann
Publisher:
Total Pages: 163
Release: 1968
Genre:
ISBN:

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First of a series of studies concerned with the value of participation in a non-atomic game. The value of an n-person game is a function that associates to each player a number that, intuitively speaking, represents an a priori opinion of what it is worth to him to play in the game. A non-atomic game is a special kind of infinite-person game, in which no individual player has any special significance. Such games have recently attracted attention as models for mass phenomena in economics. The extended definition of value is formulated in terms of simple axiomatic properties, such as symmetry, linearity, and positivity. Questions of existence and uniqueness are considered. For a certain class of games where the non-atomic measures are vectors rather than scalars, an explicit formula is derived that enables the value to be calculated directly. (Author).