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:

Published: 1968

Total Pages: 163

ISBN-13:

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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).

Values of Non-atomic Games
Values of Non-atomic Games

Author: Robert J. Aumann

Publisher:

Published: 1969

Total Pages: 0

ISBN-13:

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The paper reports the second study in a series concerned with the value of participation in a non-atomic game. A non-atomic game is a special type of infinite-person game in which no individual player has significant influence on the outcome. The work develops the concept of mixing value and presents a new approach based on mixing transformations. A program is outlined for imposing a probability measure on the space of all measurable orders. Some consideration is given to the asymptotic approach, in which a game with a continuum is treated as a limit of games with finitely many players. It is significant that all values defined in the axiomatic, mixing, and asymptotic approaches possess a common diagonal property.

Values of Non-Atomic Games
Values of Non-Atomic Games

Author: Robert J. Aumann

Publisher: Princeton University Press

Published: 2015-03-08

Total Pages: 348

ISBN-13: 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.

Game Theory and Applications
Game Theory and Applications

Author: Tatsuro Ichiishi

Publisher: Academic Press

Published: 2014-06-28

Total Pages: 449

ISBN-13: 1483295052

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Game Theory and Applications outlines game theory and proves its validity by examining it alongside the neoclassical paradigm. This book contends that the neoclassical theory is the exceptional case, and that game theory may indeed be the rule. The papers and abstracts collected here explore its recent development and suggest new research directions. Explains many of the recent central developments in game theory Highlights new research directions in economic theory which surpass the neoclassical paradigm Includes game-theoretical analyses in economics, political science, and biology Written by leading game theorists, economists, political scientists, and biologists