Values of Non-Atomic Games, IV

The Value and the Core

by Robert J. Aumann, Lloyd S. Shapley

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The fourth study in a series concerned with the value of participation in a nonatomic game, a special kind of infinite person game in which no individual player can significantly influence the outcome. The study develops the relationship between the value concept, originally defined only for finite-person games, and the core, another solution concept. The core of a game is the set of outcomes that, intuitively speaking, no coalition of players can improve upon. The object of the present study is to prove that under suitable assumptions, the core of a nonatomic game consists of a single outcome and that this outcome coincides with the value. The assumptions (superadditivity and homogeneity of degree 1) are satisfied in many cases of interest, including a basic economic application.

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