Values of Non-Atomic Games, Part II

The Random Order Approach

by Robert J. Aumann, Lloyd S. Shapley


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The second study in a series concerned with the value of participation in a nonatomic game. A nonatomic game is a special type of infinite-person game in which no individual player has significant influence on the outcome. This 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. (See also RM-5468.)

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