Accession Number : AD0711036

Title :   VALUES OF NON-ATOMIC GAMES, III: VALUES AND DERIVATIVES,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Aumann,Robert J. ; Shapley,Lloyd S.

Report Date : JUN 1970

Pagination or Media Count : 45

Abstract : A non-atomic game is a special kind of infinite-person game, in which no individual player has significance; such games have recently attracted attention as models for mass phenomena in economics. In this Memorandum, the characteristic function of the game is extended to a space that includes not only the ordinary coalitions (measurable sets) of players, but also certain 'ideal' coalitions--intuitively, sets to which a player can 'belong' at any intensity between 0 and 1. The value of the game is then redefined in terms of the derivatives of this extended function, following the principle that a player's value is based upon his incremental worth to coalitions. The close relation between this definition and those previously considered is established. (Author)

Descriptors :   (*GAME THEORY, MEASURE THEORY), SET THEORY, DIFFERENCE EQUATIONS, MAPPING(TRANSFORMATIONS), PROBABILITY, DECISION THEORY, ASYMPTOTIC SERIES, ECONOMICS, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE