Values of Non-Atomic Games, Part I

The Axiomatic Approach

by Robert J. Aumann, Lloyd S. Shapley


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First of a series of studies concerned with the value of participation in a nonatomic 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 nonatomic 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 nonatomic measures are vectors rather than scalars, an explicit formula is derived that enables the value to be calculated directly.

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