Values of Non-Atomic Games, Part II

The Random Order Approach

Robert J. Aumann, Lloyd S. Shapley

ResearchPublished 1969

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.)

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1969
  • Pages: 84
  • Document Number: RM-5842-PR

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Aumann, Robert J. and Lloyd S. Shapley, Values of Non-Atomic Games, Part II: The Random Order Approach. Santa Monica, CA: RAND Corporation, 1969. https://www.rand.org/pubs/research_memoranda/RM5842.html.
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