Abstract
In this paper, a weaker version of the Symmetry Axiom on BV, and values on subspaces of BV are discussed. Included are several theorems and examples.
Highlights
AND STATEMENT OF RESULTS.It has been shown by Aumann and Shapley [I] that there is no value defined on the entire space BV
It was shown in Ruckle [2] that there do exist continuous, efficient projections from BV onto FA which satisfy a weaker form of the Symmetry Axiom
Let (I,C) denote a standard measureable space which will remain fixed throughout the discussion
Summary
It has been shown by Aumann and Shapley [I] that there is no value defined on the entire space BV. It was shown in Ruckle [2] that there do exist continuous, efficient projections from BV onto FA which satisfy a weaker form of the Symmetry Axiom. A game v will be called a valueable game if G(v) is a measure group. The proof of the result of Aumann and Shapley cited in the first paragraph can be analyzed as follows: First it is shown that G is not a measure group.
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